Hypothesis Tests 3

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| By TerryWasley
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TerryWasley
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Quizzes Created: 1 | Total Attempts: 2,747
| Attempts: 2,747
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  • 1/9 Questions

    Hypotheses in a significance test are always stated in terms of the population parameters.

    • True
    • False
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Hypothesis Tests 3 - Quiz
About This Quiz

Hypothesis Tests 3 delves into the fundamentals of statistical hypothesis testing, focusing on p-values, t-tests, and confidence intervals. This quiz assesses understanding of statistical significance and parameter estimation, crucial for students in advanced statistics courses.

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  • 2. 

    A t-test is used when the population standard deviation for a mean is unknown. 

    • True

    • False

    Correct Answer
    A. True
    Explanation
    A t-test is used when the population standard deviation for a mean is unknown because it allows us to make inferences about the population mean using a sample mean. When the population standard deviation is unknown, the t-test uses the sample standard deviation to estimate it, providing a more accurate measure of uncertainty. This is in contrast to the z-test, which requires knowledge of the population standard deviation. Therefore, the statement that a t-test is used when the population standard deviation for a mean is unknown is true.

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  • 3. 

    Review: The critical value (z*) used for a 99% confidence interval for a sample mean when the population standard deviation is known is 2.576

    • True

    • False

    Correct Answer
    A. True
    Explanation
    The critical value (z*) is used to determine the margin of error in a confidence interval. In this case, a 99% confidence interval is being calculated for a sample mean with a known population standard deviation. The critical value for a 99% confidence level is 2.576. Therefore, the given statement is true.

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  • 4. 

    If a p-value for a 2-sided test equals .065, the p-value for the 1-sided test using the same sample data will not be significant at the 1% level.

    • True

    • False

    Correct Answer
    A. True
    Explanation
    If the p-value for a two-sided test is 0.065, then the p-value for a one-sided test would be half of that, assuming the effect is in the predicted direction, because the two-sided test allocates half of the alpha level to each tail of the distribution. So, for a one-sided test, the p-value would be 0.065 / 2 = 0.0325.
    Even though the p-value for a one-sided test would be lower than the two-sided test, it would not be significant at the 1% level (0.01), as 0.0325 is greater than 0.01. Therefore, the statement is true.

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  • 5. 

    If the results of a hypothesis test are significant at the 1% level then they are also significant at the 5% level

    • True

    • False

    Correct Answer
    A. True
    Explanation
    If the results of a hypothesis test are significant at the 1% level, it means that the probability of obtaining the observed results by chance is very low (less than 1%). Since the 5% level is less strict than the 1% level, if the results are significant at the 1% level, they will also be significant at the 5% level. This is because if the results are unlikely to occur by chance at a 1% level, they will also be unlikely to occur at a 5% level. Therefore, the statement is true.

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  • 6. 

    If the p-value is .013, the probability that Ho is true is only .013

    • True

    • False

    Correct Answer
    A. False
    Explanation
    The statement is false because the p-value is not the probability that Ho (null hypothesis) is true. The p-value is the probability of obtaining the observed data or more extreme results, assuming that the null hypothesis is true. It is used to determine the statistical significance of the results and make decisions regarding the rejection or acceptance of the null hypothesis. The p-value does not provide direct information about the probability of the null hypothesis being true.

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  • 7. 

    When a p-value is high, this means there is strong evidence against the null hypothesis

    • True

    • False

    Correct Answer
    A. False
    Explanation
    When a p-value is high, it means that there is not enough evidence to reject the null hypothesis. This implies that the observed data is consistent with the null hypothesis being true. In other words, a high p-value suggests that the results are likely due to chance and not a result of the alternative hypothesis. Therefore, the statement "there is strong evidence against the null hypothesis" is incorrect.

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  • 8. 

    When a sample statistic is close to the believed population parameter, the p-value for a significance test will typically be low. 

    • True

    • False

    Correct Answer
    A. False
    Explanation
    When a sample statistic is close to the believed population parameter, it suggests that the null hypothesis is likely to be true. In this case, the p-value for a significance test will typically be high, indicating that the observed data is likely to occur by chance alone and not due to a significant effect. Therefore, the correct answer is false.

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  • 9. 
    If a 95% confidence interval for a population mean is (8.67, 11.26) then a 2-sided test for the hypothesis  will most likely find evidence to reject Ho at the 5% level. - ProProfs

    If a 95% confidence interval for a population mean is (8.67, 11.26) then a 2-sided test for the hypothesis  will most likely find evidence to reject Ho at the 5% level.

    • True

    • False

    Correct Answer
    A. False
    Explanation
    The given confidence interval (8.67, 11.26) suggests that the population mean is likely to fall within this range. Therefore, it is unlikely that a 2-sided test for the hypothesis would find evidence to reject the null hypothesis (Ho) at the 5% level. The correct answer is False.

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  • Current Version
  • Apr 23, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Mar 15, 2013
    Quiz Created by
    TerryWasley
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