Question 1

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.Which of the following hypotheses is relevant to this claim? A) H₀: µ₁- µ₂ ≤ 0,H_A: µ₁- µ₂ > 0 B) H₀: µ₁- µ₂ ≥ 0,H_A: µ₁- µ₂ < 0 C) H₀: p₁- p₂ ≤ 0,H_A: p₁- p₂ > 0 D) H₀: p₁- p₂ ≥ 0,H_A: p₁- p₂ < 0

Accepted Answer

Since we want to determine the difference in incidence of smoking between men and women, which involves a categorical variable (smoking status), we should use a hypothesis test for proportions. Therefore, options A and B, which use the symbol µ for population means, are not appropriate. 
Between options C and D, option D is correct because we are interested in testing if one proportion (women smokers) is greater than another proportion (men smokers), and the alternative hypothesis must reflect this by using the inequality of "greater than". Therefore, D is the correct choice.

Question 2

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 µ₁and µ₂ represent the average amount of nitrogen per batch for fertilizer's A and B,respectively.Which of the following is the correct value of the test statistic? A) t₆ = −1.5617 B) t₆ = 1.5617 C) z = −1.5617 D) z = 1.5617

Accepted Answer

The correct value of the test statistic is a z-score because the population standard deviations are known. The formula for the z-score in this context is $z = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$, where $\bar{x}_1$ and $\bar{x}_2$ are the sample means, $\sigma_1$ and $\sigma_2$ are the population standard deviations, and $n_1$ and $n_2$ are the sample sizes. Given that $\bar{x}_1 = 23$, $\bar{x}_2 = 18$, $\sigma_1 = 4$, $\sigma_2 = 5$, and $n_1 = n_2 = 4$, the calculation will result in a positive z-score, indicating that the mean of distributor A's fertilizer is higher than that of distributor B's, consistent with option D.

Question 3

A restaurant chain has two locations in a medium-sized town and,believing that it has oversaturated the market for its food,is considering closing one of the restaurants.The manager of the restaurant with a downtown location claims that his restaurant generates more revenue than the sister restaurant by the freeway.The CEO of this company,wishing to test this claim,randomly selects 36 monthly revenue totals for each restaurant.The revenue data from the downtown restaurant have a mean of $360,000 and a standard deviation of $50,000,while the data from the restaurant by the freeway have a mean of $340,000 and a standard deviation of $40,000.Assume there is no reason to believe the population standard deviations are equal,and let μ₁ and μ₂ denote the mean monthly revenue of the downtown restaurant and the restaurant by the freeway,respectively.At the 5% significance level,does the evidence support the manager's claim? A) No,because the test statistic value is less than the critical value. B) Yes,because the test statistic value is less than the critical value. C) No,because the test statistic value is greater than the critical value. D) Yes,because the test statistic value is greater than the critical value.

Accepted Answer

To determine if the evidence supports the manager's claim, we can conduct a two-sample t-test for the difference in means. The null hypothesis (H0) would state that there is no difference in mean monthly revenue between the two restaurants (μ1 - μ2 = 0), while the alternative hypothesis (Ha) would claim that the downtown restaurant has a higher mean monthly revenue (μ1 - μ2 > 0). Given the sample means, standard deviations, and sizes, we calculate the test statistic. If the test statistic is greater than the critical value from the t-distribution at the 5% significance level, we reject the null hypothesis in favor of the alternative, supporting the manager's claim. The details provided do not include the exact test statistic or critical value, but the correct interpretation is that if the test statistic is indeed greater than the critical value, it indicates the evidence supports the manager's claim that the downtown restaurant generates more revenue.

Question 4

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 because the samples would not be independent.

Accepted Answer

The answer of A particular personal trainer works primarily with...

Question 5

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 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.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 p₁- p₂. B) A hypothesis test for µ₁- µ₂. C) A matched-pairs hypothesis test. D) We are unable to conduct a hypothesis test because independent random samples of each group could not be collected.

Accepted Answer

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

Question 7

A restaurant chain has two locations in a medium-sized town and,believing that it has oversaturated the market for its food,is considering closing one of the restaurants.The manager of the restaurant with a downtown location claims that his restaurant generates more revenue than the sister restaurant by the freeway.The CEO of this company,wishing to test this claim,randomly selects 36 monthly revenue totals for each restaurant.The revenue data from the downtown restaurant have a mean of $360,000 and a standard deviation of $50,000,while the data from the restaurant by the freeway have a mean of $340,000 and a standard deviation of $40,000.Assume there is no reason to believe the population standard deviations are equal,and let μ₁ and μ₂ denote the mean monthly revenue of the downtown restaurant and the restaurant by the freeway,respectively.Which of the following is the appropriate critical value(s)to test the manager's claim at the 5% significance level? A) 1.645 B) 1.668 C) 1.960 D) 1.997

Accepted Answer

Since the population standard deviations are unknown and unequal, we must use the t-distribution for the hypothesis test. The appropriate critical value(s) for a two-tailed test at the 5% significance level with 34 degrees of freedom (df= n1+n2-2=36+36-2=70) is t=1.668, obtained from a t-distribution table or a calculator. Therefore, if the calculated t-statistic is greater than 1.668 or less than -1.668, we would reject the null hypothesis and conclude that there is evidence that the downtown restaurant generates more revenue than the restaurant by the freeway.

Question 8

Calcium is an essential nutrient for strong bones and for controlling blood pressure and heart beat.Because 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.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 Calcium is an essential nutrient for strong...

Question 9

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.Which of the following hypotheses is relevant to this claim? A) H₀: µ₁- µ₂ ≤ 0,H_A: µ₁- µ₂ > 0 B) H₀: µ₁- µ₂ ≥ 0,H_A: µ₁- µ₂ < 0 C) H₀: p₁- p₂ ≤ 0,H_A: p₁- p₂ > 0 D) H₀: p₁- p₂ ≥ 0,H_A: p₁- p₂ < 0

Accepted Answer

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

Question 10

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 estimate the standard error of

Accepted Answer

The answer of When the hypothesized difference of the population...

Question 11

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.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 p₁ and p₂ represent the proportion of borrowers who received HAMP and non-HAMP modifications that did not re-default,respectively. A) H₀: p₁- p₂ ≤ 0,H_A: p₁- p₂ > 0 B) H₀: p₁- p₂ ≥ 0,H_A: p₁- p₂ < 0 C) H₀: p₁- p₂ = 0,H_A: p₁- p₂ ≠ 0 D) H₀: p₁- p₂ > 0,H_A: p₁- p₂ ≤ 0

Accepted Answer

The null hypothesis should state that there is no difference in default rates between borrowers who received HAMP modifications and non-HAMP modifications. Therefore, the correct null hypothesis is H₀: p₁ - p₂ ≥ 0. The alternative hypothesis should state that borrowers who received HAMP modifications default less than borrowers who received non-HAMP modifications, which corresponds to the directionality of a one-tailed test. Therefore, the correct alternative hypothesis is H_A: p₁ - p₂ < 0. Among the given choices, only option B correctly presents both hypotheses.

Question 12

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 13

A restaurant chain has two locations in a medium-sized town and,believing that it has oversaturated the market for its food,is considering closing one of the restaurants.The manager of the restaurant with a downtown location claims that his restaurant generates more revenue than the sister restaurant by the freeway.The CEO of this company,wishing to test this claim,randomly selects 36 monthly revenue totals for each restaurant.The revenue data from the downtown restaurant have a mean of $360,000 and a standard deviation of $50,000,while the data from the restaurant by the freeway have a mean of $340,000 and a standard deviation of $40,000.Assume there is no reason to believe the population standard deviations are equal,and let μ₁ and μ₂ denote the mean monthly revenue of the downtown restaurant and the restaurant by the freeway,respectively.Which of the following is the correct value of the test statistic to analyze the claim? A) t₆₆ = 1.848 B) t₆₇ = 1.848 C) t₆₆ = 1.874 D) t₆₇ = 1.874

Accepted Answer

Since the population standard deviations are not equal, we should use the two-sample t-test with unequal variances. The formula for the test statistic is:
t = (x̄1 - x̄2) / sqrt((s1^2/n1) + (s2^2/n2))
Plugging in the given values, we get:
t = (360,000 - 340,000) / sqrt((50,000^2/36) + (40,000^2/36))
t = 20,000 / sqrt(694,444.4)
t ≈ 1.874
Therefore, the correct answer is C.

Question 14

Calcium is an essential nutrient for strong bones and for controlling blood pressure and heart beat.Because 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.Can we conclude that the average calcium content of the two supplements differs at the 95% confidence level? A) No,because the 95% confidence interval contains the hypothesized value of zero. B) Yes,because the 95% confidence interval contains the hypothesized value of zero. C) No,because the 95% confidence interval does not contain the hypothesized value of zero. D) Yes,because the 95% confidence interval does not contain the hypothesized value of zero.

Accepted Answer

The answer of Calcium is an essential nutrient for strong...

Question 15

Which of the following 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 appropriate conditions for conducting a hypothesis test for the difference between two population proportions under independent sampling are:
1. The samples are independent.
2. Both samples are large enough to ensure that np ≥ 10 and n(1-p) ≥ 10 for both populations.
3. The populations are approximately normal or the sample sizes are large enough for the Central Limit Theorem to apply.
Option C specifies the appropriate conditions for independent sampling, which are met if both sample sizes are large enough and if there are no dependencies between the samples. The other options either do not specify the appropriate conditions or include additional conditions that may not be necessary or sufficient for independent sampling.

Question 16

A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening.Two independent samples of 25 weeks are collected for Tuesday and Wednesday.The mean attendance on Tuesday evening is calculated as 5,500,while the mean attendance on Wednesday evening is calculated as 5,850.The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445.Which of the following is the value of the appropriate test statistic? A) z = -2.4736 B) z = 2.4736 C) t_df= -2.4736 D) t_df= 2.4736

Accepted Answer

The correct test statistic is a z-test because the population standard deviations are known. The formula for the z-test statistic in comparing two means is $z = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$. Plugging in the given values, the negative result indicates that the mean attendance on Tuesday is less than on Wednesday, which corresponds to option A.

Question 17

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 µ1and µ2 represent the average amount of nitrogen per batch for fertilizer's A and B,respectively.Which of the following is an appropriate p-value?
A) 0.0592
B) 0.0847
C) 0.0896
D) 0.1184

Accepted Answer

We can use a two-sample t-test to determine if there is a significant difference in the average amount of nitrogen per batch between the two distributors.

The null hypothesis is that the average amount of nitrogen per batch is the same for both distributors:

H0: µ1 = µ2

The alternative hypothesis is that the average amount of nitrogen per batch is greater for distributor A:

Ha: µ1 > µ2

We can use a two-sample t-test with unequal variances since the population standard deviations are different:

t = (x̄1 - x̄2) / √[(s1^2/n1) + (s2^2/n2)]

where x̄1 and x̄2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values given in the problem, we get:

t = (23 - 18) / √[(4^2/4) + (5^2/4)] = 2.38

The degrees of freedom, using the formula:

df = [(s1^2/n1 + s2^2/n2)^2] / [(s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1)]

are approximately 5.

Using a t-table with 5 degrees of freedom and a one-tailed test, we find the critical value to be 1.833 (at a significance level of 0.05).

The p-value is the probability of getting a t-value as extreme or more extreme than 2.38 under the null hypothesis. Using a t-table or a calculator, we find the p-value to be 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 distributor A's fertilizer contains more nitrogen per batch than distributor B's fertilizer.

Question 18

A restaurant chain has two locations in a medium-sized town and,believing that it has oversaturated the market for its food,is considering closing one of the restaurants.The manager of the restaurant with a downtown location claims that his restaurant generates more revenue than the sister restaurant by the freeway.The CEO of this company,wishing to test this claim,randomly selects 36 monthly revenue totals for each restaurant.The revenue data from the downtown restaurant have a mean of $360,000 and a standard deviation of $50,000,while the data from the restaurant by the freeway have a mean of $340,000 and a standard deviation of $40,000.Assume there is no reason to believe the population standard deviations are equal,and let μ₁ and μ₂ denote the mean monthly revenue of the downtown restaurant and the restaurant by the freeway,respectively.Which of the following hypotheses should be used to test the manager's claim? A) H₀: µ₁- µ₂ ≤ 0,H_A: µ₁- µ₂ > 0 B) H₀: µ₁- µ₂ ≥ 0,H_A: µ₁- µ₂ < 0 C) H₀: µ₁- µ₂ = 0,H_A: µ₁- µ₂ ≠ 0 D) H₀: µ₁- µ₂ > 0,H_A: µ₁- µ₂ ≤ 0

Accepted Answer

The manager's claim that the downtown restaurant generates more revenue than the sister restaurant by the freeway is directly tested by the hypothesis in choice A, where the null hypothesis (H0) suggests no difference or the downtown restaurant making less or equal revenue, and the alternative hypothesis (Ha) suggests the downtown restaurant makes more revenue than the freeway restaurant.

Question 19

A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening.Two independent samples of 25 weeks are collected for Tuesday and Wednesday.The mean attendance on Tuesday evening is calculated as 5,500,while the mean attendance on Wednesday evening is calculated as 5,850.The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445.What are the appropriate hypotheses to determine whether there is a difference in attendance for shows on Tuesday evening and Wednesday evening? Use Tuesday attendance as population 1 mean μ₁ and Wednesday attendance as population 2 mean μ₂,or μ_D as the mean difference in matched-pairs sampling. A) H₀: µ_D ≥ 0,H_A: µ_D<0 B) H₀: µ_D = 0,H_A: µ_D≠0 C) H₀: µ₁- µ₂ = 0,H_A: µ₁- µ₂ ≠ 0 D) H₀: µ₁- µ₂ ≥ 0,H_A: µ₁- µ₂ < 0

Accepted Answer

The appropriate hypotheses in this scenario are H₀: µ₁- µ₂ = 0,H_A: µ₁- µ₂ ≠ 0. This is a two-sample t-test for the difference in means between two independent populations, with equal variances not assumed. The null hypothesis states that there is no difference in attendance between shows on Tuesday evening and Wednesday evening, while the alternative hypothesis states that there is a difference. Choice A is incorrect because it suggests a one-sided alternative hypothesis without specifying the direction of the difference. Choice B is incorrect because it suggests testing for a difference in means without specifying the direction of the difference. Choice D is incorrect because it suggests a one-sided alternative hypothesis with the wrong direction specified.

Question 20

Which of the following set of hypotheses is used to test if the mean of the first population is smaller than the mean of the second population,using matched-paired sampling? A) H₀: µ₁- µ₂ ≤ 0,H_A: µ₁- µ₂ > 0 B) H₀: µ₁- µ₂ ≥ 0,H_A: µ₁- µ₂ < 0 C) H₀: µ_D≤0,H_A: µ_D > 0 D) H₀: µ_D≥0,H_A: µ_D < 0

Accepted Answer

In matched-paired sampling, we test the difference between paired observations. To test if the mean of the first population is smaller than the second, we use H0: µD ≥ 0 and HA: µD < 0, where µD is the mean of the differences.

Quiz 10: Statistical Inference Concerning Two Populations

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.Which of the following hypotheses is relevant to this claim?

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?

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

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.Which of the following hypotheses is relevant to this claim?

When the hypothesized difference of the population proportions is equal to 0,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?

Which of the following is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling.

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