Question 1

In the test for comparing two population means when population variances are unknown and unequal,a student calculates the degrees of freedom using the proper formula as 34.7.How many degrees of freedom should the student assume to find the p-value of the test?
A)34
B)34.7
C)35
D)None of the Above

Accepted Answer

When degrees of freedom are not a whole number, they are typically rounded down to the nearest whole number for conservative estimation in statistical tests.

Question 2

What type of data is required to compare prices of the same textbooks sold by two different vendors?
A)Dependent random samples with qualitative data
B)Dependent random samples with quantitative data
C)Independent random samples with qualitative data
D)Independent random samples with quantitative data

Accepted Answer

The answer of What type of data is required to...

Question 3

When testing the difference between two population means under independent sampling,we use the z distribution if ____________.
A)The population variances are known
B)The population variances are unknown,but assumed to be equal
C)The population variances are unknown and cannot be assumed equal
D)Both A and B

Accepted Answer

When testing the difference between two population means under independent sampling, we use the z distribution if the population variances are known. This is because we can use the pooled variance estimate to calculate the standard error of the difference between the sample means. However, if the population variances are unknown, we need to use the t distribution instead.

Question 4

Assume the competing hypotheses take the following form:  versus  ,where  is the population mean for population 1 and  is the population mean for population 2.Also assume that the populations are normally distributed and we use independent sampling.The population variances are not known and cannot be assumed equal.The value of the appropriate test statistic is computed as ____________.
A) 
B) 
C) 
D)

Accepted Answer

This question is asking for the test statistic for a two-sample t-test with unequal variances. The formula for this test statistic is:

t = (x̄_1 - x̄_2) / sqrt[(s_1^2 / n_1) + (s_2^2 / n_2)]

where x̄_1 and x̄_2 are the sample means, s_1 and s_2 are the sample standard deviations, and n_1 and n_2 are the sample sizes for populations 1 and 2, respectively.

Without any information about the sample means, standard deviations, or sizes, we cannot calculate the test statistic directly. However, we do know that the populations are normally distributed and that the variances are not assumed to be equal. This suggests that we should use a two-sample t-test with unequal variances.

The answer choice that corresponds to this test statistic formula is B, 11eaa4ae_7ab7_ec78_9180_ef13c1c42bfc_TB2339_11.

Question 5

If the sampling distribution of  cannot be assumed normal,we _____________.
A)Are unable to compute a confidence interval
B)Are still able to use the z distribution to compute a confidence interval
C)Must use the t distribution with  degrees of freedom to compute a confidence interval
D)Must use the t distribution and calculate the degrees of freedom using

Accepted Answer

The answer of If the sampling distribution of  cannot...

Question 6

A particular bank has two loan modification programs for distressed borrowers: Home Affordable Modification Program (HAMP)modifications,where the federal government pays the bank $1,000 for each successful modification,and non-HAMP modifications,where the bank does not receive a bonus from the federal government.In order to qualify for a HAMP modification,borrowers must meet a set of financial suitability criteria.Define the null and alternative hypotheses to test whether borrowers who receive HAMP modifications default less than borrowers who receive non-HAMP modifications.Let  and  represent the proportion of borrowers who received HAMP and non-HAMP modifications that did not re-default,respectively.
A) 
B) 
C) 
D)

Accepted Answer

The answer of A particular bank has two loan modification...

Question 7

What type of data should be collected when examining a situation in which two candidates running in different elections are being compared in their likelihood of winning their elections?
A)Matched-pairs sampling with qualitative data
B)Matched-pairs sampling with quantitative data
C)Independent sampling with qualitative data
D)Independent sampling with quantitative data

Accepted Answer

The answer of What type of data should be collected...

Question 8

A particular personal trainer works primarily with track and field athletes.She believes that her clients run faster after going through her program for six weeks.How might she test that claim? A)A hypothesis test for . B)A hypothesis test for . C)A matched pairs hypothesis test for μ_D. D)We are unable to conduct a hypothesis test since the samples would not be independent.

Accepted Answer

The best way to test the trainer's claim is by conducting a matched pairs hypothesis test for the difference in running speed before and after the program. This will account for any individual differences and control for extraneous variables. A and B are not specific enough and do not address the need for a comparison of before and after the program. D is not applicable since a matched pairs test accounts for the lack of independence between the samples.

Question 9

Exhibit 10.1 A farmer uses a lot of fertilizer to grow his crops.The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does.He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch.Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch.Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch,respectively.Assume the distribution of nitrogen in fertilizer is normally distributed.Let  and  represent the average amount of nitrogen per batch for fertilizer's A and B,respectively. Refer to Exhibit 10.1.Calculate the appropriate p-value.
A)0.0592
B)0.0847
C)0.0896
D)0.1184

Accepted Answer

We want to conduct a two-tailed hypothesis test of the difference in means between the two populations, with a null hypothesis of equal means and an alternate hypothesis of unequal means. Using a two-sample t-test with the given data and assuming equal variances, we get a t-value of 2.08 and a p-value of 0.0592. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean amount of nitrogen per batch is different for the two distributors. Therefore, the appropriate p-value is 0.0592.

Question 10

A particular bank has two loan modification programs for distressed borrowers: Home Affordable Modification Program (HAMP)modifications,where the federal government pays the bank $1,000 for each successful modification,and non-HAMP modifications,where the bank does not receive a bonus from the federal government.In order to qualify for a HAMP modification,borrowers must meet a set of financial suitability criteria.What type of hypothesis test should we use to test whether borrowers from this particular bank who receive HAMP modifications are more likely to re-default than those who receive non-HAMP modifications?
A)A hypothesis test for  .
B)A hypothesis test for  .
C)A matched-pairs hypothesis test.
D)We are unable to conduct a hypothesis test since independent random samples of each group could not be collected.

Accepted Answer

The answer of A particular bank has two loan modification...

Question 11

Exhibit 10.2.Calcium is an essential nutrient for strong bones and for controlling blood pressure and heart beat.Since most of the body's calcium is stored in bones and teeth,the body withdraws the calcium it needs from the bones.Over time,if more calcium is taken out of the bones than is put in,the result may be thin,weak bones.This is especially important for women who are often recommended a calcium supplement.A consumer group activist assumes that calcium content in two popular supplements are normally distributed with the same unknown population variance,and uses the following information obtained under independent sampling: Let μ₁ and μ₂ denote the corresponding population means. Refer to Exhibit 10.2.Construct a 95% confidence interval for the difference μ₁ - μ₂. A)[-30.9386,1.0614] B)[-31.5886,-0.4114] C)[-33.8007,1.8007] D)[-34.8012,2.8012]

Accepted Answer

The answer of Exhibit 10.2.Calcium is an essential nutrient for...

Question 12

Which of the following set of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population,using matched-paired sampling?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Which of the following set of hypotheses...

Question 13

Assume the competing hypotheses take the following form:  versus  ,where  is the population mean for population 1 and  is the population mean for population 2.Also assume that the populations are normally distributed with known variances and we use independent sampling.The value of the appropriate test statistic is computed as ___________.
A) 
B) 
C) 
D)

Accepted Answer

The appropriate test statistic for independent sample t-test with known variances and normally distributed populations is calculated as:
t = (x̄1 – x̄2) / √ [(s1^2/n1) + (s2^2/n2)]
where,
x̄1 and x̄2 are the sample means
s1^2 and s2^2 are the sample variances
n1 and n2 are the sample sizes.

Here, the sample means are not given, so we cannot calculate the test statistic. Therefore, the answer is not A, B, or D.

Question 14

What type of test for population means should be performed when examining a situation in which employees are first tested,then trained,and finally retested?
A)A z test under independent sampling with known population variances
B)A t test under independent sampling with unknown but equal population variances
C)A t test under dependent sampling
D)A t test under independent sampling with unknown and unequal population variances

Accepted Answer

In this situation, the employees are being tested twice - once before training and once after training. This means that the two samples are dependent on each other, as they come from the same group of individuals. Therefore, a t test under dependent sampling should be performed.

Question 15

When the hypothesized difference of the population proportions is equal to 0,we ____________.
A)Use a matched-pairs approach
B)Are able to estimate the standard error of  using the pooled

C)Can use the confidence interval to implement the test if the difference of the population proportions is equal to 0
D)Both B and C

Accepted Answer

When the hypothesized difference of the population proportions is equal to 0, we can estimate the standard error of the difference using the pooled proportion, which is the mean of the two sample proportions. Additionally, we can use the confidence interval to implement the test if the difference of the population proportions is equal to 0. Therefore, both options B and C are correct. The matched-pairs approach (option A) is used when we have paired data, and it is not relevant when testing the difference of population proportions.

Question 16

Exhibit 10.1 A farmer uses a lot of fertilizer to grow his crops.The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does.He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch.Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch.Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch,respectively.Assume the distribution of nitrogen in fertilizer is normally distributed.Let  and  represent the average amount of nitrogen per batch for fertilizer's A and B,respectively. Refer to Exhibit 10.1.Calculate the value of the test statistic.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Exhibit 10.1 A farmer uses a lot...

Question 17

You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood.Let men and women be represented by populations 1 and 2,respectively.The relevant hypotheses are constructed as _____________.
A) 
B) 
C) 
D)

Accepted Answer

The answer of You would like to determine if there...

Question 18

It is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling:
A)In every case.
B)Only if  and
 .
C)Only if  and
 .
D)Only if

Accepted Answer

The answer of It is appropriate to conduct a hypothesis...

Question 19

You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood.Let women and men be represented by populations 1 and 2,respectively.The relevant hypotheses are constructed as ____________.
A) 
B) 
C) 
D)

Accepted Answer

The answer of You would like to determine if there...

Question 20

Assume the competing hypotheses take the following form:  versus  ,where  is the population mean for population 1 and  is the population mean for population 2.Also assume that the populations are normally distributed and that the observations in the two samples are independent.The population variances are not known but are assumed equal.The value of the appropriate test statistic is computed as ____________.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Assume the competing hypotheses take the following...

Quiz 10: Statistical Inference Concerning Two Populations

In the test for comparing two population means when population variances are unknown and unequal,a student calculates the degrees of freedom using the proper formula as 34.7.How many degrees of freedom should the student assume to find the p-value of the test?

What type of data is required to compare prices of the same textbooks sold by two different vendors?

When testing the difference between two population means under independent sampling,we use the z distribution if ____________.

If the sampling distribution of cannot be assumed normal,we _____________.

What type of data should be collected when examining a situation in which two candidates running in different elections are being compared in their likelihood of winning their elections?

A particular personal trainer works primarily with track and field athletes.She believes that her clients run faster after going through her program for six weeks.How might she test that claim?

Which of the following set of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population,using matched-paired sampling?

What type of test for population means should be performed when examining a situation in which employees are first tested,then trained,and finally retested?

When the hypothesized difference of the population proportions is equal to 0,we ____________.

You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood.Let men and women be represented by populations 1 and 2,respectively.The relevant hypotheses are constructed as _____________.

It is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling:

You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood.Let women and men be represented by populations 1 and 2,respectively.The relevant hypotheses are constructed as ____________.