Test your Knowledge on Inferences and Proportions Quiz!

1. Which of these is NOT one of the conditions that must be checked for one-proportion hypothesis tests?

The products np and n(1-p) are greater than or equal to 10.

The alpha must be 0.05.

The data are from a SRS of independent observations

The population is at least 10 times as large as the sample

All of the other choices are described in the text. The SRS requirement allows us to make inferences. The np, n(1-p) test permits us to use the normal approximation to this admittedly binomial setting. The large population requirement reduces the effect of extreme values on our std deviation-allowing us to use the formula for the std dev SQRT(p(1-p)/n) instead of somethin more complicated.

Explanation

All of the other choices are described in the text. The SRS requirement allows us to make inferences. The np, n(1-p) test permits us to use the normal approximation to this admittedly binomial setting. The large population requirement reduces the effect of extreme values on our std deviation-allowing us to use the formula for the std dev SQRT(p(1-p)/n) instead of somethin more complicated.

2. Two sets of 60 high school students each were taught algebra by two methods, respectively. The experimental group used programmed learning and no formal lectures; the control group was given formal lectures by a teacher. At the end of the experiment, both groups were given a standardized test, and the number of students scoring above 85% was recorded: 41 out of 60 of the experimental group had scores above 85%; 24 out of 60 in the control group had scores above 85%. Test the hypothesis that the two groups were not different in their performance on the standardized test. Which procedure would be most appropriate for testing the data?

Wo-sample z-test for means

Two-sample t-test for means

One sample z-test for proportion

Two sample z-test for proportions

Linear Regression t-test

The most appropriate procedure for testing the data in this scenario is the two-sample z-test for proportions. This is because we are comparing the proportions of students scoring above 85% in two different groups (experimental and control). The z-test for proportions allows us to determine if there is a significant difference between the proportions of students in each group who scored above 85%.

Explanation

The most appropriate procedure for testing the data in this scenario is the two-sample z-test for proportions. This is because we are comparing the proportions of students scoring above 85% in two different groups (experimental and control). The z-test for proportions allows us to determine if there is a significant difference between the proportions of students in each group who scored above 85%.

3. When constructing a one-proportion confidence interval (a confidence interval for one proportion), we use the value of p-hat

When calculating the standard error of p-hat

As the point estimate for the population parameter, p

For checking our assumptions/conditions before constructing the interval

In all of these cases

They are all true! You always use the best information possible for the value in each of these cases. For a 1-proportion interval, in the absence of a hypothesized value for p, we use the next best thing--the sample proportion.

Explanation

They are all true! You always use the best information possible for the value in each of these cases. For a 1-proportion interval, in the absence of a hypothesized value for p, we use the next best thing--the sample proportion.

4. You are given the difference between pretest and posttest measures for a set of participants. You believe that there is no improvement from pre- to post-test.

Sample confidence interval for the mean

Sample confidence interval for the difference of proportions

Proportion confidence interval

Sample hypotheses test for the difference of proportions

Paired t-test

The paired t-test is the appropriate statistical test in this scenario because it is used to compare the means of two related groups. In this case, the pretest and posttest measures are related because they are taken from the same set of participants. The paired t-test allows us to determine if there is a significant difference between the means of the two measures, which would indicate whether there is an improvement or not from pre- to post-test.

Explanation

The paired t-test is the appropriate statistical test in this scenario because it is used to compare the means of two related groups. In this case, the pretest and posttest measures are related because they are taken from the same set of participants. The paired t-test allows us to determine if there is a significant difference between the means of the two measures, which would indicate whether there is an improvement or not from pre- to post-test.

5.

You are given x and n from a random sample and you want an estimate for the population proportion.

Sample confidence interval for the mean

sample confidence interval for the difference of proportions

Proportion confidence interval

Sample hypotheses test for the difference of proportions

Paired t-test

To estimate the population proportion, a proportion confidence interval is used. This interval provides an estimate of the range within which the true population proportion is likely to fall. It is calculated using the sample proportion, the sample size, and a chosen level of confidence. The proportion confidence interval is a commonly used method to estimate population proportions when working with random samples.

Explanation

To estimate the population proportion, a proportion confidence interval is used. This interval provides an estimate of the range within which the true population proportion is likely to fall. It is calculated using the sample proportion, the sample size, and a chosen level of confidence. The proportion confidence interval is a commonly used method to estimate population proportions when working with random samples.

6. For a two-sample confidence interval, we have the following information: x1, n1, x2, and n2. What do we check to make sure that we can use a normal approximation?

X1 and x2 are > 5

X1 > 5 and x2 > 5

X1 & x2 > 5

X1 > 5 & x2 > 5

Both x1 and x2 are greater than 5

To use a normal approximation for a two-sample confidence interval, we need to ensure that both sample sizes (n1 and n2) are large enough. In this case, we are given x1, n1, x2, and n2, but we need to check if x1 and x2 are greater than 5. This is because the Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean becomes approximately normal, regardless of the shape of the population distribution. Therefore, if both x1 and x2 are greater than 5, we can assume that the sample sizes are large enough to use a normal approximation.

Explanation

To use a normal approximation for a two-sample confidence interval, we need to ensure that both sample sizes (n1 and n2) are large enough. In this case, we are given x1, n1, x2, and n2, but we need to check if x1 and x2 are greater than 5. This is because the Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean becomes approximately normal, regardless of the shape of the population distribution. Therefore, if both x1 and x2 are greater than 5, we can assume that the sample sizes are large enough to use a normal approximation.

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7. A vegetable canner claims that the mean fill per 16-ounce can is 16.1 ounces. Several underweight complaints have been lodged against the company, and the canner wants to see if the machine set for the fill mechanism is correct. That is, he wishes to test the hypothesis that µ = 16.1 ounces. Experience with the machine has shown that the variation in fill observed over a number of years is σ =.11 ounces. A random sample of n = 10 cans gave the following measurements in ounces: 16.1, 16.0, 16.2, 15.9, 16.0, 16.1, 16.1, 15.9, 16.1, 16.0. Do these data indicate that µ differs from 16.1 ounces? Which would be the appropriate testing procedure for this scenario?

One-sample z-test for a mean

One-sample t-test for a mean

Two-sample t-test for means

One sample z-test for proportion

Hi-Square Test for Goodness of Fit

The appropriate testing procedure for this scenario is a one-sample z-test for a mean. This is because we are given the population standard deviation (σ) and we want to test if the sample mean (x̄) differs from a specified value (16.1 ounces). In a one-sample z-test, we use the sample mean, population mean, and population standard deviation to calculate the z-score, which is then compared to the critical value to determine if there is a significant difference.

Explanation

The appropriate testing procedure for this scenario is a one-sample z-test for a mean. This is because we are given the population standard deviation (σ) and we want to test if the sample mean (x̄) differs from a specified value (16.1 ounces). In a one-sample z-test, we use the sample mean, population mean, and population standard deviation to calculate the z-score, which is then compared to the critical value to determine if there is a significant difference.

8. You are given x-bar(1)and x-bar(2),s(1), s(2), n(1), n(2) from two independent samples and you want an estimate of the difference between the two population means.

Sample t-confidence interval for the mean

Sample t-confidence interval for the difference of means

Proportion confidence interval

sample hypotheses t-test for the difference of means

Paired t-test

The sample t-confidence interval for the difference of means is the most appropriate choice in this scenario because it allows us to estimate the difference between the two population means using the sample means, standard deviations, and sample sizes from the two independent samples. This interval takes into account the variability within each sample and provides a range of values within which we can be confident that the true difference between the population means lies.

Explanation

The sample t-confidence interval for the difference of means is the most appropriate choice in this scenario because it allows us to estimate the difference between the two population means using the sample means, standard deviations, and sample sizes from the two independent samples. This interval takes into account the variability within each sample and provides a range of values within which we can be confident that the true difference between the population means lies.

9. Which estimate for the proportion is used when performing a two-sample hypothesis test of p1 = p2? Assume that you are given x1, n1, x2, and n2.

The pooled sample proportion

(x1 + x2)/(n1 + n2)

(x1+x2)/(n1+n2)

The sum of the successes divided by the sum of the attempts

The correct answer is the pooled sample proportion, (x1 + x2)/(n1 + n2), which is calculated by adding the number of successes from both samples (x1 and x2) and dividing it by the total number of attempts from both samples (n1 and n2). This estimate is used in a two-sample hypothesis test of proportions to estimate the common proportion for both populations being compared. By pooling the data from both samples, it provides a more accurate estimate of the true population proportion.

Explanation

The correct answer is the pooled sample proportion, (x1 + x2)/(n1 + n2), which is calculated by adding the number of successes from both samples (x1 and x2) and dividing it by the total number of attempts from both samples (n1 and n2). This estimate is used in a two-sample hypothesis test of proportions to estimate the common proportion for both populations being compared. By pooling the data from both samples, it provides a more accurate estimate of the true population proportion.

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10. Ten sets of identical twins, all wanting to learn French, were divided into two groups, each group containing one of each twin pair. Group 1 was flown to France, where they lived for one month. Group 2 was enrolled in an intensive French course at a local university. At the end of one month, all subjects were given a standard French language exam. Which procedure is appropriate for performing the analysis of the exam scores?

One-sample z-test for a mean

Two-sample z-test for means

One-sample t-test for a mean

Two-sample t-test for means

One sample z-test for proportion

The appropriate procedure for performing the analysis of the exam scores is a one-sample t-test for a mean. This is because the study involves comparing the exam scores of one group (Group 1) to a known population mean (the average exam score). The t-test is used when the population standard deviation is unknown, which is the case here. By conducting a one-sample t-test, we can determine if the exam scores of Group 1 are significantly different from the population mean.

Explanation

The appropriate procedure for performing the analysis of the exam scores is a one-sample t-test for a mean. This is because the study involves comparing the exam scores of one group (Group 1) to a known population mean (the average exam score). The t-test is used when the population standard deviation is unknown, which is the case here. By conducting a one-sample t-test, we can determine if the exam scores of Group 1 are significantly different from the population mean.

Test Your Knowledge On Inferences And Proportions Quiz!