Question 1

The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by some non-zero number.

Accepted Answer

The pooled proportion estimate is used when the null hypothesis assumes that the two population proportions are equal, not when they are assumed to differ by a non-zero number.

Question 2

Pooling is made possible by hypothesizing (under the null hypothesis)that p₁ = p₂.

Accepted Answer

Pooling is based on the assumption that the population proportions of the two groups (with and without the trait of interest) are equal, so the null hypothesis is that p₁ = p₂. Therefore, the statement is true.

Question 3

The difference in two sample proportions is an unbiased consistent estimator of the difference in their respective population proportions.

Accepted Answer

This statement is true. The difference in two sample proportions is an unbiased estimator of the difference in their respective population proportions, and as the sample size increases, the estimator becomes more precise and consistent.

Question 4

For testing the difference between two population proportions,the pooled proportion estimate should be used to compute the value of the test statistic when the:

Accepted Answer

The pooled proportion estimate should be used to compute the value of the test statistic when the null hypothesis states that the two population proportions are equal. The pooled proportion estimate assumes that the true proportions in both populations are equal and estimates this common proportion using data from both populations. This helps to increase the precision of the estimate and improve the accuracy of the test statistic, leading to more reliable results. When the null hypothesis is not that the proportions are equal, such as in a one-sided test or when sample sizes are very small, other methods may be more appropriate.

Question 5

The pooled proportion estimate is used when:

Accepted Answer

The pooled proportion estimate is used under the assumption that the two population proportions are equal under the null hypothesis, which is not explicitly stated in any of the given choices. Choices A, B, and C do not accurately describe the conditions for using a pooled proportion estimate.

Question 6

A required condition for using the normal approximation to the binomial in testing the difference between two population proportions is that n₁p₁ ≥ 30 and n₂p₂ ≥ 30.

Accepted Answer

The correct condition for using the normal approximation to the binomial in testing the difference between two population proportions is that both $n_1p_1(1-p_1) \geq 10$ and $n_2p_2(1-p_2) \geq 10$, where $n_1$ and $n_2$ are the sample sizes, and $p_1$ and $p_2$ are the sample proportions for the two groups being compared. The threshold value is generally considered to be 10, not 30.

Question 7

The pooled proportion estimate is found by taking the proportion of successes from sample 1 plus the proportion of successes from sample 2.

Accepted Answer

The pooled proportion estimate is found by taking the total number of successes from both samples combined and dividing by the total number of observations from both samples combined, not by simply adding the proportions of successes from each sample.

Question 8

In comparing two population means the statistic under consideration is  .

Accepted Answer

The answer of In comparing two population means the statistic...

Question 9

Antioxidants 
A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B,and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below  ​ ​
-{Antioxidants Narrative} Develop the 95% confidence interval estimate of the ratio of the two population variances.

Accepted Answer

The answer of Antioxidants 
A food processor wants to compare...

Question 10

For testing the difference between two population proportions,the pooled proportion estimate is found by taking:

Accepted Answer

The pooled proportion estimate is found by calculating the total number of successes in both samples and dividing it by the total of both sample sizes. This gives us an estimate of the proportion of successes for the combined population. This estimate is used to calculate the standard error and test for statistical significance between the two sample proportions. Option A is incorrect because we cannot simply add the proportions from each sample as this will not give us an accurate estimate. Option C is incorrect because it does not involve calculating a pooled proportion estimate. Option D is incorrect because there is a correct choice.

Question 11

The expected value of the difference between two sample proportions is the difference between their corresponding population proportions.

Accepted Answer

This statement is true. The expected value of the difference between two sample proportions is equal to the difference between their corresponding population proportions, under the assumption of unbiased sampling and independence between the samples. This is a result of the properties of the sampling distribution of sample proportions and the law of large numbers.

Question 12

The variance of the difference in sample proportions equals the difference of their population variances.

Accepted Answer

The variance of the difference in sample proportions is equal to the sum of their population variances divided by their sample sizes.

Question 13

Antioxidants 
A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B,and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below  ​ ​
-{Antioxidants Narrative} Determine the rejection region for testing the equality of the two population variances at α = .05.

Accepted Answer

The answer of Antioxidants 
A food processor wants to compare...

Question 14

Antioxidants 
A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B,and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below  ​ ​
-{Antioxidants Narrative} Explain how to use the 95% confidence interval for testing the equality of the two population variances at the 5% level.

Accepted Answer

The answer of Antioxidants 
A food processor wants to compare...

Question 15

The pooled proportion estimate is used when the proportion of successes from sample 1 equals the proportion of successes from sample 2.

Accepted Answer

The pooled proportion estimate is used to combine information from two samples to get an overall estimate of the proportion in the entire population, not necessarily because the proportions of successes in the two samples are equal. It is often used in hypothesis testing for comparing two proportions.

Question 16

Clinic Waiting Time
 In a random sample of 20 patients who visited a clinic at Medical Center 1,a researcher found that the variance of the waiting time (in minutes)was 128.0.In a random sample of 15 patients in the clinic of Medical Center 2,the researcher found the variance to be 178.8. ​ ​
-{Clinic Waiting Time Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.

Accepted Answer

The answer of Clinic Waiting Time
 In a random sample...

Question 17

In constructing a confidence interval estimate for the difference between two population proportions,we pool the population proportions when the populations are normally distributed.

Accepted Answer

Pooling the population proportions is done based on the assumption of equal population proportions for the two groups, not on the normal distribution of the populations.

Question 18

Antioxidants 
A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B,and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below  ​ ​
-{Antioxidants Narrative} State the null and alternative hypotheses for determining if the population variances differ for Antioxidants A and B.

Accepted Answer

The answer of Antioxidants 
A food processor wants to compare...

Question 19

In constructing a confidence interval estimate for the difference between two population proportions,we:

Accepted Answer

The answer of In constructing a confidence interval estimate for...

Question 20

Antioxidants 
A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B,and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below  ​ ​
-{Antioxidants Narrative} Calculate the value of the test statistic for testing the equality of the population variances,and write the proper conclusion.

Accepted Answer

The answer of Antioxidants 
A food processor wants to compare...

Quiz 13: Inference About Comparing Two Populations

The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by some non-zero number.

Pooling is made possible by hypothesizing (under the null hypothesis)that p1 = p2.

The difference in two sample proportions is an unbiased consistent estimator of the difference in their respective population proportions.

For testing the difference between two population proportions,the pooled proportion estimate should be used to compute the value of the test statistic when the:

The pooled proportion estimate is used when:

A required condition for using the normal approximation to the binomial in testing the difference between two population proportions is that n1p1 ≥ 30 and n2p2 ≥ 30.

The pooled proportion estimate is found by taking the proportion of successes from sample 1 plus the proportion of successes from sample 2.

In comparing two population means the statistic under consideration is .

For testing the difference between two population proportions,the pooled proportion estimate is found by taking:

The expected value of the difference between two sample proportions is the difference between their corresponding population proportions.

The variance of the difference in sample proportions equals the difference of their population variances.

The pooled proportion estimate is used when the proportion of successes from sample 1 equals the proportion of successes from sample 2.

In constructing a confidence interval estimate for the difference between two population proportions,we pool the population proportions when the populations are normally distributed.

In constructing a confidence interval estimate for the difference between two population proportions,we:

Pooling is made possible by hypothesizing (under the null hypothesis)that p₁ = p₂.

A required condition for using the normal approximation to the binomial in testing the difference between two population proportions is that n₁p₁ ≥ 30 and n₂p₂ ≥ 30.