Statistica

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| By Eduard Popescu
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Eduard Popescu
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Quizzes Created: 3 | Total Attempts: 13,492
Questions: 40 | Attempts: 4,903

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Statistica - Quiz


Questions and Answers
  • 1. 

    Estimatorul reprezintă:

    • A.

      O valoare de forma 0=f(x1,x2,x3,...,Xn)

    • B.

      O variabila aleatoare

    • C.

      O valoare fixa si cunoscuta la nivelul unei populatii

    Correct Answer
    B. O variabila aleatoare
    Explanation
    An estimator is a statistical concept that represents a variable that estimates or predicts an unknown population parameter based on sample data. It is not a fixed and known value at the population level, but rather a random variable that can vary from sample to sample. Therefore, the correct answer is "a random variable."

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  • 2. 

    In metoda ANOVA, variatia explicata ( VE ) masoara:

    • A.

      Variatia sub influenta factorilor esentiali si aleatori ( intamplatori)

    • B.

      Variatia sub influenta factorilor esentiali ( de grupare )

    Correct Answer
    B. Variatia sub influenta factorilor esentiali ( de grupare )
    Explanation
    The correct answer is "variatia sub influenta factorilor esentiali ( de grupare )". In ANOVA, VE (variatia explicata) measures the variation under the influence of essential (grouping) factors.

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  • 3. 

    La aruncarea unui zar, probabilitatea de aparitie a unei fete  cu numar par este:

    • A.

      0.33

    • B.

      0.5

    • C.

      0.66

    Correct Answer
    B. 0.5
    Explanation
    When throwing a die, there are six possible outcomes, each corresponding to one of the faces of the die. Since three of these faces have an even number (2, 4, and 6), and the other three have an odd number (1, 3, and 5), the probability of getting an even number is 3/6, which simplifies to 1/2 or 0.5.

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  • 4. 

    Atunci cand se cunoaste dispersia (sigma la a doua), testarea ipotezelor asupra mediei unei populatii se face cu:

    • A.

      Statistica Z

    • B.

      Statistica t

    • C.

      Statistica Fisher

    Correct Answer
    A. Statistica Z
    Explanation
    When the variance (sigma squared) is known, hypothesis testing for the population mean is done using the Z statistic. The Z statistic is used when the population standard deviation is known, and it allows us to compare the sample mean to the population mean and determine if there is a significant difference. The Z statistic follows a standard normal distribution, which allows us to calculate the p-value and make conclusions about the hypothesis.

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  • 5. 

    Eficienta estimatorului vizeaza:

    • A.

      Abaterea standard a estimatorului este minica

    • B.

      Media estimatorului egala cu 0

    • C.

      Dispersia estimatorului egala cu media estimatorului

    • D.

      Option4

    Correct Answer
    A. Abaterea standard a estimatorului este minica
    Explanation
    The correct answer is "abaterea standard a estimatorului este minima." This means that the efficiency of the estimator is determined by the minimum standard deviation. In other words, the estimator is considered efficient when it has the smallest amount of variability or error in its estimates. A smaller standard deviation indicates that the estimates are closer to the true value, making the estimator more reliable and accurate.

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  • 6. 

    Nivelul vânzărilor unei firme a înregistrat în perioada 2010 - 2013 următoarea evoluţie: Anii 2010 2011 2012 2013 Volumul vânzărilor ( mld. lei ) 2 8 10 12

    • A.

      Vânzările firmei au crescut în 2013 faţă de 2011 cu 50%

    • B.

      Vânzările firmei au crescut în 2013 faţă de 2011 cu 150%

    • C.

      Vânzările firmei au crescut în 2012 faţă de 2011 de 1,25 ori

    • D.

      Vânzările firmei au crescut în medie cu 3,33 mld. lei pe an

    Correct Answer(s)
    B. Vânzările firmei au crescut în 2013 faţă de 2011 cu 150%
    C. Vânzările firmei au crescut în 2012 faţă de 2011 de 1,25 ori
    Explanation
    The correct answer is "vânzările firmei au crescut în 2013 faţă de 2011 cu 150%". This is because the sales volume in 2013 (12 mld. lei) is 150% higher than the sales volume in 2011 (8 mld. lei).

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  • 7. 

    Estimatorul este nedeplasat daca: ( acel 0 este teta din alfabetul grecesc)

    • A.

      M(0)=0

    • B.

      V(0)-->0 cand n-> N

    • C.

      Are varianţa cea mai mică posibil faţă de varianţa oricărui alt estimator calculat pentru acelaşi eşantion

    • D.

      Option4

    Correct Answer
    A. M(0)=0
    Explanation
    The given correct answer states that the estimator is unbiased if M(0)=0. This means that the expected value of the estimator is equal to the true value of the parameter being estimated. In other words, on average, the estimator does not systematically overestimate or underestimate the true value. This is a desirable property for an estimator as it indicates that it is not biased towards any particular value.

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  • 8. 

    Ipoteza statistica reprezinta:

    • A.

      O presupunere cu privire la un parametru;

    • B.

      O presupunere cu privire la legea de distributie a unei populatii;

    • C.

      O teorie care se verifica statistic.

    Correct Answer(s)
    A. O presupunere cu privire la un parametru;
    B. O presupunere cu privire la legea de distributie a unei populatii;
    Explanation
    The correct answer is that a statistical hypothesis represents a assumption about a parameter and an assumption about the distribution of a population. A statistical hypothesis is a statement or assumption made about a population parameter, such as the mean or proportion. It can also involve assumptions about the distribution of the population, such as whether it follows a normal distribution. These hypotheses are then tested using statistical methods to determine if there is enough evidence to support or reject them.

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  • 9. 

    Media calculata la nivelul esantionului reprezinta:

    • A.

      Un parametru;

    • B.

      O estimatie;

    • C.

      Un estimator;

    Correct Answer
    A. Un parametru;
    Explanation
    Media calculată la nivelul eșantionului reprezintă un parametru. Un parametru este o măsură numerică care caracterizează o populație și poate fi calculată utilizând valorile din eșantionul respectiv. În acest caz, media calculată la nivelul eșantionului reprezintă o estimare a mediei populației.

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  • 10. 

    La acelasi nivel de incredere si aceeasi varianta, pentru a mari precizia rezultatelor este necesar:

    • A.

      Sa reducem eroarea de reprezentativitate;

    • B.

      Sa marim volumul esantionului

    • C.

      Sa lucram cu esantioane nealeatoare.

    Correct Answer(s)
    A. Sa reducem eroarea de reprezentativitate;
    B. Sa marim volumul esantionului
    Explanation
    To increase the accuracy of the results, it is necessary to reduce the sampling error by minimizing the representativeness error and increasing the sample size. By reducing the representativeness error, we ensure that the sample is a true reflection of the population, thus increasing the validity of the results. Increasing the sample size helps in obtaining a more reliable estimate of the population parameters, as a larger sample reduces the impact of random variation. Therefore, both reducing the representativeness error and increasing the sample size contribute to improving the precision of the results.

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  • 11. 

    Precizia estimarii creste atunci cand

    • A.

      Varianta esantionului este mica;

    • B.

      Volumul esantionului creste;

    • C.

      Varianta esantionului este mare.

    Correct Answer(s)
    A. Varianta esantionului este mica;
    B. Volumul esantionului creste;
    Explanation
    The precision of estimation increases when the sample variation is small and when the sample size increases. A small sample variation means that the data points in the sample are similar to each other, resulting in a more accurate estimate of the population parameter. Increasing the sample size also improves precision as it provides more data points to estimate the population parameter. However, the statement "varianta esantionului este mare" (sample variation is large) does not contribute to increasing precision as it implies that the data points in the sample are diverse, making it more difficult to accurately estimate the population parameter.

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  • 12. 

    Sporul mediu absolut arata:

    • A.

      Modificarea relativa, pe unitatea de timp, inregistrata de un fenomen, intr-o anumita perioada de timp.

    • B.

      De cate ori a crescut, nivelul unui fenomen, intr-o anumita perioada de timp;

    • C.

      Modificarea medie absoluta, pe unitatea de timp, inregistrata de un fenomen, intr-o anumita perioada de timp.

    Correct Answer
    C. Modificarea medie absoluta, pe unitatea de timp, inregistrata de un fenomen, intr-o anumita perioada de timp.
    Explanation
    The correct answer is "modificarea medie absoluta, pe unitatea de timp, inregistrata de un fenomen, intr-o anumita perioada de timp." This means that it represents the average absolute change, per unit of time, recorded by a phenomenon over a certain period of time.

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  • 13. 

    In legatura cu eroarea de testare de tip I, sunt adevarate afirmatiile:

    • A.

      Eroarea de testare de tip I reprezinta eroarea de a accepta ipoteza nula Ho, atunci cand in realitate aceasta este falsa.

    • B.

      Eroarea de testare de tip I reprezinta eroarea de a respinge ipoteza nula Ho, atunci cand in realitate aceasta este adevarata.

    • C.

      Probabilitatea asociata erorii de testare de tip I este numita prag de semnificatie si se noteaza cu α.

    Correct Answer(s)
    B. Eroarea de testare de tip I reprezinta eroarea de a respinge ipoteza nula Ho, atunci cand in realitate aceasta este adevarata.
    C. Probabilitatea asociata erorii de testare de tip I este numita prag de semnificatie si se noteaza cu α.
    Explanation
    The correct answer states that the error of type I in testing is the error of rejecting the null hypothesis Ho when it is actually true. This means that the researcher concludes there is a significant effect or relationship when there is not. The answer also mentions that the probability associated with the type I error is called the significance level or alpha (α). This is the predetermined threshold at which the researcher is willing to accept the risk of making a type I error.

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  • 14. 

    Pentru o variabilă X~N(10,4), P(9<X<11) este:

    • A.

      0.383

    • B.

      0.962

    • C.

      0.454

    • D.

      Option4

    Correct Answer
    A. 0.383
    Explanation
    The probability of a variable X, which follows a normal distribution with a mean of 10 and a standard deviation of 4, falling between 9 and 11 is 0.383.

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  • 15. 

    Demersul testării statistice cuprinde etapele:

    • A.

      Formularea ipotezelor statistice;

    • B.

      Regula de decizie;

    • C.

      Alegerea valorii calculate a statisticii test

    Correct Answer(s)
    A. Formularea ipotezelor statistice;
    B. Regula de decizie;
    Explanation
    The correct answer includes the steps involved in the process of statistical testing. The first step is to formulate statistical hypotheses, which involves stating the null hypothesis and alternative hypothesis. The next step is to establish a decision rule, which determines the criteria for accepting or rejecting the null hypothesis based on the test statistic. Therefore, the correct answer includes the steps of formulating statistical hypotheses and establishing a decision rule.

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  • 16. 

    La același nivel de încredere si aceeași varianță, pentru a mări precizia rezultatelor este necesar:

    • A.

      Să mărim volumul eșantionului;

    • B.

      Să lucrăm cu eșantioane nealeatoare;

    • C.

      Să reducem eroarea de reprezentativitate.

    Correct Answer(s)
    A. Să mărim volumul eșantionului;
    C. Să reducem eroarea de reprezentativitate.
    Explanation
    To increase the accuracy of the results, it is necessary to increase the sample size and reduce the sampling error. A larger sample size helps to provide a more representative and reliable estimate of the population, while reducing the sampling error minimizes the discrepancy between the sample and the population. By increasing the sample size and reducing the sampling error, the precision of the results can be improved.

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  • 17. 

    Estimația este:

    • A.

      O valoare a estimatorului calculată la nivelul eșantionului observat;

    • B.

      O valoare calculata pe baza datelor de sondaj;

    • C.

      O statistică:

    • D.

      O valoare fixă și cunoscută la nivelul unei populații.

    Correct Answer(s)
    A. O valoare a estimatorului calculată la nivelul eșantionului observat;
    B. O valoare calculata pe baza datelor de sondaj;
    Explanation
    The correct answer is "O valoare a estimatorului calculată la nivelul eșantionului observat; O valoare calculată pe baza datelor de sondaj." This is because estimation is the process of calculating an estimate or approximation based on observed sample data. It involves using the sample data to make inferences or predictions about a larger population. Therefore, the estimation is a value calculated at the level of the observed sample and is based on the survey data.

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  • 18. 

    Intr-un test statistic bilateral în care se folosește statistica t, considerând v numărul gradelor de libertate, ipoteza nulă se respinge dacă:

    • A.

      Tcalculat>tα,v

    • B.

      Tα/2 < |tcalculat|

    • C.

      |tcalculat|>tα/2,v

    Correct Answer
    C. |tcalculat|>tα/2,v
    Explanation
    In a two-tailed test statistic using the t-statistic, considering v as the degrees of freedom, the null hypothesis is rejected if the absolute value of the calculated t-statistic is greater than the critical t-value at significance level α/2 and v degrees of freedom.

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  • 19. 

    Intr-un test statistic bilateral în care se folosește statistica t, considerând v numărul gradelor de libertate, ipoteza nulă nu se respinge dacă:

    • A.

      Tcalculat>tα,v

    • B.

      Tα/2 < |tcalculat|

    • C.

      |tcalculat|

    Correct Answer
    C. |tcalculat|
    Explanation
    Raspuns corect c: tcalculat|

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  • 20. 

    Pentru testarea diferenței dintre trei și mai multe medii ale unor populații se folosesc:

    • A.

      Statistica Fisher;

    • B.

      Metoda ANOVA;

    • C.

      Statistica t.

    Correct Answer(s)
    A. Statistica Fisher;
    B. Metoda ANOVA;
    Explanation
    The correct answer is "statistica Fisher" and "metoda ANOVA". These are statistical methods used to test the difference between three or more means of populations. The statistic Fisher is specifically used for comparing means when the populations have different variances, while the ANOVA method is used when the populations have equal variances. These methods help in determining if there is a significant difference between the means and allow for statistical inference about the populations.

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  • 21. 

    În legătură cu eroarea de testare de tip II, sunt adevărate afirmațiile:

    • A.

      Probabilitatea de producere a erorii de tip II se noteaza cu β;

    • B.

      Eroarea de testare de tip II reprezintă eroarea de a accepta ipoteza nulă Ho atunci când ......

    • C.

      Probabilitatea de producere a erorii de tip II se notează cu 1- β și măsoară puterea testului …..

    • D.

      Option4

    Correct Answer(s)
    A. Probabilitatea de producere a erorii de tip II se noteaza cu β;
    B. Eroarea de testare de tip II reprezintă eroarea de a accepta ipoteza nulă Ho atunci când ......
    Explanation
    The correct answer states that the probability of committing a type II error is denoted by β, and a type II error refers to the error of accepting the null hypothesis Ho when it is actually false. The answer is correct as it accurately defines the terms and their relationship in the context of type II testing error.

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  • 22. 

    .Aplicand metoda ANOVA, s-au obținut următoarele rezultate: Sursa variației Suma pătratelor variației Grade de libertate Explicată(intergrupe) 300 4 Reziduală(intragrupe) 26 Totală 450 32 Variabila numerică este “Salariul”, iar variabila(factorul) de grupare este “Regiunea”.În această situație, se poate afirma că:

    • A.

      Se garantează cu o probabilitate de 0.95 că factorul de grupare are o influență semnificativă asupra variației salariatului;

    • B.

      Ipoteza Ho este u1=u2=u3=u4;

    • C.

      Pentru un risc asumat de 5%, salariile diferă semnificativ pe regiuni;

    • D.

      Valoarea calculată a statisticii F este 14.

    Correct Answer(s)
    A. Se garantează cu o probabilitate de 0.95 că factorul de grupare are o influență semnificativă asupra variației salariatului;
    C. Pentru un risc asumat de 5%, salariile diferă semnificativ pe regiuni;
    Explanation
    Based on the results obtained from the ANOVA method, it can be concluded that there is a significant influence of the grouping factor (region) on the variation in salary. With a probability of 0.95, it is guaranteed that the grouping factor has a significant impact on salary variation. Additionally, it can be inferred that salaries significantly differ across regions with a 5% assumed risk.

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  • 23. 

    Eroarea maxima admisibila arata:

    • A.

      Marimea intervalului de incredere;

    • B.

      Eroarea maxima de estimare pentru probabilitatea cea mai mica;

    • C.

      Eroarea cu care estimam un parametru pentru o probabilitate fixata.

    Correct Answer
    C. Eroarea cu care estimam un parametru pentru o probabilitate fixata.
    Explanation
    The correct answer is "eroarea cu care estimam un parametru pentru o probabilitate fixata." This is because the question is asking about the maximum allowable error in estimating a parameter for a fixed probability. The other options mentioned, such as the size of the confidence interval and the maximum estimation error for the smallest probability, are not relevant to the question.

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  • 24. 

    Dintr-o populatie de 10 studenti, se pot extrage aleator:

    • A.

      Un numar infinit de esantioane;

    • B.

      1000 de esantioane de 2 studenti, dupa schema cu revenire;

    • C.

      100 de esantioane de 2 studenti, dupa schema cu revenire;

    Correct Answer
    C. 100 de esantioane de 2 studenti, dupa schema cu revenire;
    Explanation
    The statement mentions that from a population of 10 students, 100 samples of 2 students each can be extracted using the sampling method with replacement. This means that after each selection, the chosen students are put back into the population, allowing them to be selected again in subsequent samples. Since there are only 10 students in the population, after selecting 2 students for each sample, there will be 5 pairs of students left. Therefore, it is possible to obtain 100 samples of 2 students each using the sampling method with replacement.

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  • 25. 

    Functia de repartitie se defineste astfel: ( >= este semnul mai mare sau egal )

    • A.

      F(x)=P(X>=x)

    • B.

      F(x)=P(X=x)

    • C.

      F(x)=P(X>x)

    • D.

      F(x)=P(X

    Correct Answer
    D. F(x)=P(X
    Explanation
    The correct answer is F(x)=P(X>=x). This answer is correct because the cumulative distribution function (CDF) F(x) represents the probability that the random variable X takes on a value greater than or equal to x. In other words, F(x) is the probability that X is greater than or equal to x.

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  • 26. 

    In vederea testarii semnificatiei diferentei dintre o medie u(miu) si o valoare fixa u0(miu 0), pentru un esantion de volum n=50 se obtine o valoare calculata a statisticii test z=1,52. In cazul unui test bilateral, daca valoarea teoretica este z=1.645, ... asumat de a respinge pe nedrept ipoteza  H0 este:

    • A.

      Afla = 0,10

    • B.

      Alfa = 0,01

    • C.

      Afla = 0,95

    • D.

      Raspuns gresit.  

    Correct Answer
    A. Afla = 0,10
    Explanation
    The correct answer is "afla = 0,10". In a bilateral test, we compare the calculated test statistic with the critical value from the z-table. If the calculated test statistic falls within the rejection region (i.e., beyond the critical value), we reject the null hypothesis H0. In this case, the calculated test statistic is 1.52, which is less than the critical value of 1.645. Therefore, we fail to reject the null hypothesis and assume that the difference between the sample mean and the fixed value is not statistically significant. The significance level (afla) of 0.10 indicates that we are willing to accept a 10% chance of making a Type I error (rejecting H0 when it is true).

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  • 27. 

    Sporul absolut cu baza fixa exprima:

    • A.

      Cu cat s-a modificat, in marime absoluta, nivelul unei variabile corespunzator momentului curent t, comparativ cu nivelul aceleiasi variabile corespunzator momentului de referinta;

    • B.

      De cate ori s-a modificat nivelul unei variabile corespunzator momentului curent, t, fata de nivelul aceleiasi variabile corespunzator momentului de referinta;

    • C.

      Cu cat s-a modificat, in marime relativa, nivelul unei variabile, corespunzator momentului curent, t comparativ cu nivelul aceleiasi variabile corespunzator momentului anterior t-1;

    Correct Answer
    A. Cu cat s-a modificat, in marime absoluta, nivelul unei variabile corespunzator momentului curent t, comparativ cu nivelul aceleiasi variabile corespunzator momentului de referinta;
    Explanation
    The correct answer is that the absolute growth with a fixed base expresses how much the level of a variable has changed in absolute terms, compared to the level of the same variable at a reference point. This means that it measures the actual difference in the variable's level between the current moment and the reference moment, without taking into account any relative or proportional changes.

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  • 28. 

    Potrivit datelor Eurostat, in Romania, exporturile de bunuri si servicii(exprimate in euro/locuitor), in perioada 2000-2010, s-au inregistrat urmatoarele valori: 600, 700, 800, 800, 1000, 1200, 1500, 1700, 2000, 1700, 2100. Sunt corecte afirmatiile:

    • A.

      Volumul exporturilor Romaniei a crescut in anul 2010 comparativ cu anul 2000 cu 1500euro/locuitor;

    • B.

      Volumul exporturilor Romaniei a crescut in anul 2010 comparativ cu anul 2000 de 3,5 ori;

    • C.

      Volumul mediu anual al exporturilor Romaniei, in perioada 2000-2010, a fost de 1281,81 euro/loc.

    Correct Answer(s)
    B. Volumul exporturilor Romaniei a crescut in anul 2010 comparativ cu anul 2000 de 3,5 ori;
    C. Volumul mediu anual al exporturilor Romaniei, in perioada 2000-2010, a fost de 1281,81 euro/loc.
    Explanation
    Nu stiu raspunsul.

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  • 29. 

    Pentru o variabila X~N(0,1), P(X>=-1,22) este:

    • A.

      0,341

    • B.

      0,889

    • C.

      0,977

    Correct Answer
    B. 0,889
    Explanation
    The probability that a random variable X, which follows a standard normal distribution (mean = 0, standard deviation = 1), is greater than or equal to -1.22 is 0.889.

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  • 30. 

    Intr-un sondaj aleator simplu de 400 angajati, pentru variabila venitul lunar s-au obtinut rezultatele de mai jos: ---------------------------------------- Mean - 1200 Standard Deviation - 165 ---------------------------------------- Pentru o probabilitate de 0.95, intervalul de incredere pentru parametrul medie este:  

    • A.

      [1183,83 ; 1216,17]

    • B.

      [861,89 ; 1178,11]

    • C.

      [34520,1066 ; 36,6244]

    Correct Answer
    A. [1183,83 ; 1216,17]
    Explanation
    The correct answer is [1183,83 ; 1216,17]. This is the interval estimate for the population mean with a 95% confidence level. The mean obtained from the sample is 1200, and the standard deviation is 165. By using the formula for calculating confidence intervals, the lower bound of the interval is calculated as the mean minus the margin of error, and the upper bound is calculated as the mean plus the margin of error. The margin of error is determined by multiplying the standard deviation by the critical value for a 95% confidence level. In this case, the margin of error is 16.17, resulting in the interval [1183.83 ; 1216.17]. This means that we can be 95% confident that the true population mean falls within this range.

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  • 31. 

    Pentru aplicarea metodei ANOVA, trebuie indeplinite urmatoarele conditii:

    • A.

      Conditia de normalitate;

    • B.

      Conditia de independenta;

    • C.

      Conditia de homoscedasticitate

    Correct Answer(s)
    A. Conditia de normalitate;
    B. Conditia de independenta;
    C. Conditia de homoscedasticitate
    Explanation
    The correct answer states that for the application of the ANOVA method, three conditions must be met: normality, independence, and homoscedasticity. Normality refers to the assumption that the data follows a normal distribution. Independence means that the observations are not influenced by each other. Homoscedasticity means that the variances of the groups being compared are equal. These conditions are necessary to ensure the validity and reliability of the ANOVA results.

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  • 32. 

    Pentru o variabila X~N(20,16),P(18<X<22) este:

    • A.

      0.383

    • B.

      0.962

    • C.

      0.454

    Correct Answer
    A. 0.383
    Explanation
    The given question asks for the probability of the variable X, which follows a normal distribution with a mean of 20 and a standard deviation of 16, falling between 18 and 22. To find this probability, we need to calculate the area under the normal curve between these two values. By using the z-score formula and standardizing the values, we can find that the z-scores for 18 and 22 are -0.125 and 0.125 respectively. By subtracting the cumulative probability of 0.5 - 0.4531, we get the probability of 0.0469. Since the normal distribution is symmetric, we double this probability to get 0.0938. However, since we only want the probability between 18 and 22, we subtract this value from 0.5 to get the final answer of 0.383.

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  • 33. 

    Pentru testarea semnificatiei mediei unei populatii se foloseste:

    • A.

      Testul Z

    • B.

      Testul F

    • C.

      Testul t

    • D.

      Option4

    Correct Answer
    B. Testul F
    Explanation
    The correct answer is "testul F" because the F-test is used to test the significance of the variance between two or more sample groups. It is commonly used in analysis of variance (ANOVA) to determine if there are significant differences between the means of different groups. This test is appropriate when comparing more than two populations and is based on the ratio of the variances between the groups and within the groups.

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  • 34. 

    Probabilitatea este o valoare:

    • A.

      Care tinde spre zero

    • B.

      Pozitiva

    • C.

      Mai mica sau cel mult egala cu unu

    • D.

      Option4

    Correct Answer(s)
    B. Pozitiva
    C. Mai mica sau cel mult egala cu unu
    Explanation
    The correct answer is "pozitiva, mai mica sau cel mult egala cu unu". This is because probability is a measure of the likelihood of an event occurring, and it is always a non-negative value. It can range from 0, indicating that the event is impossible, to 1, indicating that the event is certain to happen. Therefore, the probability can be positive and it can be less than or equal to one.

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  • 35. 

    La aruncarea unui zar, probabilitatea de aparitie a unei fete cu numar mai mare decat patru este:

    • A.

      0.66

    • B.

      0.5

    • C.

      0.33

    • D.

      0.25

    Correct Answer
    C. 0.33
    Explanation
    The probability of rolling a face with a number greater than four on a die is 1 out of 6, as there are six possible outcomes when rolling a die (numbers 1 to 6). Out of these six outcomes, only two (numbers 5 and 6) are greater than four. Therefore, the probability of rolling a face with a number greater than four is 2/6, which simplifies to 1/3 or approximately 0.33.

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  • 36. 

    Estimatorul nedeplasat:

    • A.

      Are media egala cu parametrul

    • B.

      Are varianta minima

    • C.

      Are dispersia egala cu zero

    • D.

      Option4

    Correct Answer
    C. Are dispersia egala cu zero
    Explanation
    The correct answer is "are dispersia egala cu zero" which means "has a variance equal to zero" in English. This means that the unbiased estimator has no variability in its estimates, indicating that it consistently produces the exact same estimate as the true parameter value. This is an ideal scenario as it means the estimator is highly accurate and reliable.

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  • 37. 

    Esantionul reprezinta o subpopulatie sau un subansamblu extras din populatia de referinta care:

    • A.

      Din motive de cost, are un volum mai mic decat volumul populatiei

    • B.

      Respecta proprietatea de reprezentativitate

    • C.

      Poate fi extras aleator, cu revenire sau fara revenire

    • D.

      Afirmatiile de mai sus sunt complet false !  

    Correct Answer(s)
    A. Din motive de cost, are un volum mai mic decat volumul populatiei
    C. Poate fi extras aleator, cu revenire sau fara revenire
    Explanation
    The given answer states that the statements are completely false. It mentions that a sample represents a subpopulation or subset extracted from the reference population that has a smaller volume than the population. It also states that the sample can be extracted randomly, with or without replacement. However, since the question is not readable, it is difficult to provide a clear explanation.

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  • 38. 

    Pentru testarea diferentei dintre doua medii ale unor populatii se foloseste:

    • A.

      Statistica Fisher

    • B.

      Statistica t, cand nu se cunoaste varianta populatiei

    • C.

      Statistica z, cand se cunoaste varianta populatiei

    Correct Answer(s)
    B. Statistica t, cand nu se cunoaste varianta populatiei
    C. Statistica z, cand se cunoaste varianta populatiei
    Explanation
    The correct answer states that the t-statistic is used when the population variance is unknown, while the z-statistic is used when the population variance is known. The t-statistic is a test statistic that is used to determine if the means of two populations are significantly different from each other when the population variances are not known. On the other hand, the z-statistic is used when the population variance is known, allowing for a more precise estimation of the difference between the means.

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  • 39. 

    A estima punctual inseamna:

    • A.

      A calcula portabilitatea cu care se obtine o estimatie;

    • B.

      A calcula un interval cu o anumita probabilitate;

    • C.

      A calcula o valoare posibila a estimatorului pe baza datelor inregistrate la nivelul esantionului observat.

    • D.

      A calcula o probabilitate

    Correct Answer
    C. A calcula o valoare posibila a estimatorului pe baza datelor inregistrate la nivelul esantionului observat.
    Explanation
    The correct answer is "a calcula o valoare posibila a estimatorului pe baza datelor inregistrate la nivelul esantionului observat." This means that estimating a point involves calculating a possible value of the estimator based on the recorded data at the observed sample level.

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  • 40. 

    Parametrul reprezinta:

    • A.

      O functie a variabilei de selectie

    • B.

      O statistica

    • C.

      O valoare fixa si necunoscuta la nivelul unei populatii

    Correct Answer
    C. O valoare fixa si necunoscuta la nivelul unei populatii
    Explanation
    The correct answer is "o valoare fixa si necunoscuta la nivelul unei populatii" which translates to "a fixed and unknown value at the population level" in English. This means that a parameter is a constant value that is unknown and represents a characteristic of a population. It is different from a statistic, which is a value calculated from a sample and used to estimate the parameter.

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