ISDS Exam 4

[0.4534, 0.5666]

Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, she has garnered 51% support. Construct a 95% confidence interval on the population proportion for the support of candidate A in the following election. Multiple Choice - [0.4534, 0.5666] - [0.4625, 0.5575] - [0.5084, 0.5116] - [0.5086, 0.5114]

n = 246

Find the minimum sample size when we want to construct a 95% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported candidate B and 14 supported candidate C. The desired margin of error is 0.06. Multiple Choice - n = 173 - n = 174 - n = 245 - n = 246

[11.6334, 13.3666]

Given a sample mean of 12.5—drawn from a normal population, a sample of size 25, and a sample variance of 2.4—find a 99% confidence interval for the population mean. rev: 12_06_2021_QC_CS-287275 Multiple Choice - [11.7019, 13.2981] - [11.1574, 13.8426 - [11.6334, 13.3666] - [11.7279, 13.2721]

[$44.79, $63.20]

In an examination of holiday spending (known to be normally distributed) of a sample of 16 holiday shoppers at a local mall, an average of $54 was spent per hour of shopping. Based on the current sample, the standard deviation is equal to $21. Find a 90% confidence interval for the population mean level of spending per hour. Multiple Choice - [$44.83, $63.17] - [$44.79, $63.20] - [$45.36, $62.63] - [$46,96, $61.04]

10.840

In the following table, individuals are cross-classified by their age group and income level. For the chi-square test of independence, the value of the test statistic is ________. Multiple Choice - 8.779 - 10.840 - 13.243 - 16.159

False Two random samples are considered independent if the process that generates one sample is completely separate from the process that generates the other sample.

T/F: Two random samples are considered independent if the observations in the first sample are related to the observations in the second sample.

True

T/F: We convert the estimate x¯1 − x¯2 into the corresponding value of the z or t test statistic by dividing the difference between x¯1 − x¯2 and the hypothesized difference d0d0 by the standard error of the estimator X¯1 − X¯2 .

Degrees of Freedom

The ___________ determine the extent of the broadness of the tails of the distribution.

D = 0.0887

The minimum sample size n required to estimate a population proportion, with 95% confidence and the assumed most conservative pˆp^ = 0.5, was found to be 122. Which of the following is the approximate value of the assumed desired margin of error? Multiple Choice - D = 0.0055 - D = 0.0078 - D = 0.0745 - D = 0.0887

False Explanation: The sampling distribution of P¯¯¯ is based on a binomial distribution and can be approximated by a normal distribution for large samples. The null hypothesis typically corresponds to a presumed default state of nature.

T/F: The sampling distribution of P¯ is based on a normal distribution on samples of any size

True

T/F: The tdf distribution has broader tails than the z distribution.

Conclude that the mean attendance differs because the p-value = 0.0134 < 0.05.

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 appropriate decision given a 5% level of significance? Multiple Choice - Conclude that the mean attendance differs because the p-value = 0.0067 < 0.05. - Conclude that the mean attendance differs because the p-value = 0.0134 < 0.05. - Do not conclude that the mean attendance differs because the p-value = 0.0067 < 0.05. - Do not conclude that the mean attendance differs because the p-value = 0.0134 < 0.05.

[0.343, 0.377]

A Monster.com pool of 3,057 individuals asked, "What's the longest vacation you plan to take this summer?" The following relative frequency distribution summarizes the results. The 95% confidence interval for the proportion of people who plan a one-week vacation this summer is ______. Multiple Choice - [0.345, 0.375] - [0.345, 0.382] - [0.343, 0.377] - [0.338, 0.382]

[0.557, 0.603]

A Monster.com pool of 3,057 individuals asked: "What's the longest vacation you plan to take this summer?" The following relative frequency distribution summarizes the results. The 99% confidence interval for the proportion of people who plan a one-week or two-week vacation this summer is ______. Multiple Choice - [0.563, 0.603] - [0.557, 0.597] - [0.563, 0.597] - [0.557, 0.603]

[210.5992, 239.4008]

A basketball coach wants to know how many free throws an NBA player shoots during the course of an average practice. The coach takes a random sample of 43 players and finds the average number of free throws shot per practice was 225 with a standard deviation of 35. Construct a 99% confidence interval for the average number of free throws in practice. Multiple Choice - [210.5992, 239.4008] - [210.6155, 239.3845] - [211.2506, 238.7494] - [214.2290, 235.7710]

[7.9490, 8.3044]

A company that produces computers recently tested the battery in its latest laptop in six separate trials. The battery lasted 8.23, 7.89, 8.14, 8.25, 8.30, and 7.95 hours before burning out in each of the tests. Assuming the battery duration is normally distributed, construct a 95% confidence interval for the mean battery life in the new model. Multiple Choice - [7.9490, 8.3044] - [7.9575, 8.2959] - [7.9873, 8.2661] - [7.9912, 8.2622]

Margin of Error

A confidence interval is generally associated with a(n) _____________.

[0.044, 0.171]

A random sample of 130 mortgages in the state of Maryland was randomly selected. From this sample, 14 were found to be delinquent on their current payment. The 98% confidence interval for the proportion based on this sample is _______. Multiple Choice - [0.044, 0.171] - [0.036, 0.180] - [0.029, 0.188] - [0.015, 0.201]

Yes, because the confidence interval does not contain zero.

A university wants to compare out-of-state applicants' mean SAT math scores (μ1) to in-state applicants' mean SAT math scores (μ2). The university looks at 35 in-state applicants and 35 out-of-state applicants. The mean SAT math score for in-state applicants was 540, with a standard deviation of 20. The mean SAT math score for out-of-state applicants was 555, with a standard deviation of 25. It is reasonable to assume the corresponding population standard deviations are equal. At the 5% significance level, can the university conclude that the mean SAT math score for in-state students and out-of-state students differ? Multiple Choice - No, because the confidence interval contains zero. - Yes, because the confidence interval contains zero. - No, because the confidence interval does not contain zero. - Yes, because the confidence interval does not contain zero.

Fail to reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.

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 µ1 and µ2 represent the average amount of nitrogen per batch for fertilizers A and B, respectively. Which of the following is the appropriate conclusion at the 5% significance level? Multiple Choice - Reject H0; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B. - Reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B. - Fail to reject H0; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B. - Fail to reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.

The test statistic is less than the critical value; we fail to reject the null hypothesis and cannot conclude that the quality of the flash drive production and the production shift are not independent of one another.

A manufacturer of flash drives for data storage operates a production facility that runs on three 8-hour shifts per day. The following contingency table shows the number of flash drives that were defective and not defective from each shift. Based on the critical value approach and using α = 0.05, which of the following decisions and conclusions for this hypothesis test would be accurate? Multiple Choice - The test statistic is greater than the critical value; we reject the null hypothesis and cannot conclude that the quality of the flash drive production and the production shift are independent of one another. - The test statistic is greater than the critical value; we fail to reject the null hypothesis and can conclude that the quality of the flash drive production and the production shift are independent of one another. - The test statistic is less than the critical value; we fail to reject the null hypothesis and cannot conclude that the quality of the flash drive production and the production shift are not independent of one another. - The test statistic is less than the critical value; we reject the null hypothesis and cannot conclude that the quality of the flash drive production and the production shift are independent of one another.

2.125

A manufacturer of flash drives for data storage operates a production facility that runs on three 8-hour shifts per day. The following contingency table shows the number of flash drives that were defective and not defective from each shift. The test statistic for this test of independence is ______. Multiple Choice - 2.125 - 1.225 - 2.152 - 2.521

Reject H0: µ1 − µ2 ≤ 0 and therefore conclude that relative to the 1981 levels, 6- to 12-year-old children spent less time in 2021 on household chores.

A new study has found that, on average, 6- to 12-year-old children are spending less time on household chores today compared to 1981 levels. Suppose two samples representative of the study's results report the following summary statistics for the two periods. Using a 5% confidence level, which of the following is correct? Multiple Choice - Reject H0: µ1 − µ2 ≤ 0 and therefore do not conclude that relative to the 1981 levels, 6- to 12-year-old children spent less time in 2021 on household chores. - Do not reject H0: µ1 − µ2 ≤ 0 and therefore conclude that relative to the 1981 levels, 6- to 12-year-old children spent less time in 2021 on household chores. - Reject H0: µ1 − µ2 ≤ 0 and therefore conclude that relative to the 1981 levels, 6- to 12-year-old children spent less time in 2021 on household chores. - Do not reject H0: µ1 − µ2 ≤ 0 and therefore do not conclude that relative to the 1981 levels, 6- to 12-year-old children spent less time in 2021 on household chores.

t58 = 5.73

A new study has found that, on average, 6- to 12-year-old children are spending less time on household chores today compared to 1981 levels. Suppose two samples representative of the study's results report the following summary statistics for the two periods. Which of the following is the correct value of the test statistic assuming that the unknown population variances are equal? Multiple Choice - z = −5.73 - t58 = 5.73 - z = 5.73 - t59 = −5.73

t34 = −1.8734

A producer of fine chocolates believes that the sales of two varieties of truffles differ significantly during the holiday season. The first variety is milk chocolate while the second is milk chocolate filled with mint. It is reasonable to assume that truffle sales are normally distributed with unknown but equal population variances. Two independent samples of 18 observations each are collected for the holiday period. A sample mean of 12 million milk chocolate truffles sold with a sample standard deviation of 2.5 million. A sample mean of 13.5 million truffles filled with mint sold with a sample standard deviation of 2.3 million. Use milk chocolate as population 1 and mint chocolate as population 2. Assuming the population variances are equal, which of the following is the value of the appropriate test statistic? Multiple Choice - z = −1.8734 - z = 1.8734 - t34 = −1.8734 - t34 = 1.8734

Do not conclude that the average milk chocolate and mint chocolate sales differ because the p-value is greater than 0.05.

A producer of fine chocolates believes that the sales of two varieties of truffles differ significantly during the holiday season. The first variety is milk chocolate while the second is milk chocolate filled with mint. It is reasonable to assume that truffle sales are normally distributed with unknown but equal population variances. Two independent samples of 18 observations each are collected for the holiday period. A sample mean of 12 million milk chocolate truffles sold with a sample standard deviation of 2.5 million. A sample mean of 13.5 million truffles filled with mint sold with a sample standard deviation of 2.3 million. Use milk chocolate as population 1 and mint chocolate as population 2. Which of the following is the appropriate decision given a 5% level of significance? Multiple Choice - Conclude that the average milk chocolate and mint chocolate sales differ because the p-value is greater than 0.05. - Conclude that the average milk chocolate and mint chocolate sales do not differ because the p-value is less than 0.05. - Do not conclude that the average milk chocolate and mint chocolate sales differ because the p-value is greater than 0.05. - Do not conclude that the average milk chocolate and mint chocolate sales do not differ because the p-value is less than 0.05.

Yes, because the test statistic value is greater than the critical value.

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? Multiple Choice - No, because the test statistic value is less than the critical value. - Yes, because the test statistic value is less than the critical value. - No, because the test statistic value is greater than the critical value. - Yes, because the test statistic value is greater than the critical value.

1.668

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? Multiple Choice - 1.645 - 1.668 - 1.960 - 1.997

t66 = 1.874

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? Multiple Choice - t66 = 1.848 - t67 = 1.848 - t66 = 1.874 - t67 = 1.874

[0.3192, 0.3608]

A sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year. Construct a 90% confidence interval of the proportion of American households who expect to buy a new car next year. Multiple Choice - [0.3152, 0.3648] - [0.3192, 0.3608] - [0.3394, 0.3406] - [0.3354, 0.3446]

[0.3105, 0.3695]

A sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year. Construct a 98% confidence interval of the proportion of American households who expect to buy a new car next year. Multiple Choice - [0.3074, 0.3726] - [0.3105, 0.3695] - [0.3140, 0.3660] - [0.3392, 0.3408]

[0.2116, 0.2484]

A sample of 2,007 American adults was asked how they viewed China, with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy." Construct a 95% confidence interval of the proportion of American adults who viewed China as either "unfriendly" or "an enemy." Multiple Choice - [0.2013, 0.2587] - [0.2116, 0.2484] - [0.2146, 0.2454] - [0.2208, 0.2392]

[0.0463, 0.0737]

A sample of 2,007 American adults was asked how they viewed China, with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy." Construct a 99% confidence interval of the proportion of American adults who viewed China as "an enemy." Multiple Choice - [0.0463, 0.0737] - [0.0476, 0.0724] - [0.0512, 0.0688] - [0.0597, 0.0603]

t70 = 2.811

A statistics professor at a large university hypothesizes that students who take statistics in the morning typically do better than those who take it in the afternoon. He takes a random sample of 36 students who took a morning class and, independently, another random sample of 36 students who took an afternoon class. He finds that the morning group scored an average of 74 with a standard deviation of 8, while the evening group scored an average of 68 with a standard deviation of 10. The population standard deviation of scores is unknown but is assumed to be equal for morning and evening classes. Let µ1 and µ2 represent the population mean final exam scores of statistics' courses offered in the morning and the afternoon, respectively. Compute the appropriate test statistic to analyze the claim at the 1% significance level. Multiple Choice - t70 = −2.811 - t70 = 2.811 - z = −2.811 - z = 2.811

[0.4057, 0.5543]

Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 98 supported candidate B and 58 supported candidate C. Construct a 99% confidence interval on the population proportion for the support of candidate A in the following election. Multiple Choice - [0.4057, 0.5543] - [0.4130, 0.5470] - [0.4779, 0.4821] - [0.4781, 0.4819]

[−25.7961, −4.2039]

A university wants to compare out-of-state applicants' mean SAT math scores (μ1) to in-state applicants' mean SAT math scores (μ2). The university looks at 35 in-state applicants and 35 out-of-state applicants. The mean SAT math score for in-state applicants was 540, with a standard deviation of 20. The mean SAT math score for out-of-state applicants was 555, with a standard deviation of 25. It is reasonable to assume the corresponding population standard deviations are equal. Calculate a 95% confidence interval for the difference μ1 - μ2. Multiple Choice - [−25.6067,−4.3933] - [−25.7961, −4.2039] - [−25.8124, −4.1876] - [−33.6105, 3.6105]

[56.4216, 63.5784]

A website advertises job openings on its website, but job seekers have to pay to access the list of job openings. The website recently completed a survey to estimate the number of days it takes to find a new job using its service. It took the last 30 customers an average of 60 days to find a job. Assume the population standard deviation is 10 days. Calculate a 95% confidence interval of the population mean number of days it takes to find a job. Multiple Choice - [40.4000, 79.6000] - [55.9085, 64.0915] - [56.4216, 63.5784] - [56.9966, 63.0034]

the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease

According to a report in USA Today, more and more parents are helping their young adult children get homes. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population proportion, then __________. Multiple Choice - the resulting margin of error will increase and the risk of reporting an incorrect interval will increase - the resulting margin of error will decrease and the risk of reporting an incorrect interval will increase - the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease - the resulting margin of error will decrease and the risk of reporting an incorrect interval will decrease

n = 188

According to a report in USAToday, more and more parents are helping their young adult children buy homes. You would like to construct a 90% confidence interval of the proportion of all young adults in Louisville, Kentucky, who received help from their parents in buying a home. How large a sample should you take so that the margin of error is no more than 0.06? Multiple Choice - n = 114 - n = 188 - n = 267 - Cannot be determined.

[2.5167, 2.9033]

At a particular academically challenging high school, the average GPA of a high school senior is known to be normally distributed. After a sample of 20 seniors is taken, the average GPA is found to be 2.71 and the variance is determined to be 0.25. Find a 90% confidence interval for the population mean GPA. Multiple Choice - [2.5167, 2.9033] - [2.5261, 2.8961] - [2.5615, 2.8585] - [2.6358, 2.7842]

No, because the 95% confidence interval contains the hypothesized value of zero.

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? Multiple Choice - No, because the 95% confidence interval contains the hypothesized value of zero. - Yes, because the 95% confidence interval contains the hypothesized value of zero. - No, because the 95% confidence interval does not contain the hypothesized value of zero. - Yes, because the 95% confidence interval does not contain the hypothesized value of zero.

[−34.8012, 2.8012]

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. Multiple Choice - [−30.9386, 1.0614] - [−31.5886, −0.4114] - [−33.8007, 1.8007] - [−34.8012, 2.8012]

[0.4625, 0.5575]

Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 153 supported her. Construct a 90% confidence interval on the population proportion for the support of candidate A in the following election. Multiple Choice - [0.4534, 0.5666] - [0.4625, 0.5575] - [0.5086, 0.5114] - [0.5090, 0.5110]

True

T/F: The margin of error in the confidence interval for the difference μ1−μ2 equals the standard error se(X¯1−X¯2) multiplied by either zα/2 or tα/2,dft depending on whether or not the population variances are known.

Reject H0: µ1 − µ2 ≤ 0 and therefore conclude that on average men spend more money than women on St. Patrick's Day.

Do men really spend more money on St. Patrick's Day as compared to women? A recent survey found that men spend an average of $43.87 while women spend an average of $29.54. Assume that these data were based on a sample of 100 men and 100 women and the population standard deviations of spending for men and women are $32 and $25, respectively. Using 1% confidence level, which of the following is the correct conclusion for this test? Multiple Choice - Reject H0: µ1 − µ2 ≤ 0 and therefore do not conclude that on average men spend more money than women on St. Patrick's Day. - Do not reject H0: µ1 − µ2 ≤ 0 and therefore conclude that on average men spend more money than women on St. Patrick's Day. - Reject H0: µ1 − µ2 ≤ 0 and therefore conclude that on average men spend more money than women on St. Patrick's Day. - Do not reject H0: µ1 − µ2 ≤ 0 and therefore do not conclude that on average men spend more money than women on St. Patrick's Day.

z = 3.53

Do men really spend more money on St. Patrick's Day as compared to women? A recent survey found that men spend an average of $43.87 while women spend an average of $29.54. Assume that these data were based on a sample of 100 men and 100 women and the population standard deviations of spending for men and women are $32 and $25, respectively. Which of the following is the correct value of test statistic? Multiple Choice - z = −3.53 - tdf = 3.53 - tdf = −3.53 - z = 3.53

reject the null hypothesis; age and income are dependent

In the following table, individuals are cross-classified by their age group and income level. Using the critical value approach, the decision and conclusion are _________________________________________. Multiple Choice - do not reject the null hypothesis; age and income are dependent - do not reject the null hypothesis; age and income are independent - reject the null hypothesis; age and income are dependent - reject the null hypothesis; age and income are independent

reject the null hypothesis; age and income are dependent

In the following table, individuals are cross-classified by their age group and income level. Using the p-value approach and α = 0.05, the decision and conclusion are __________________________________. Multiple Choice - do not reject the null hypothesis; age and income are dependent - do not reject the null hypothesis; age and income are independent - reject the null hypothesis; age and income are dependent - reject the null hypothesis; age and income are independent

reject the null hypothesis; gender and candidate preference are dependent

In the following table, likely voters' preferences of two candidates are cross-classified by gender. Using the p-value approach and α = 0.10, the decision and conclusion are ___________________________________. Multiple Choice - reject the null hypothesis; gender and candidate preference are dependent - do not reject the null hypothesis; gender and candidate preference are independent - reject the null hypothesis; gender and candidate preference are independent - do not reject null hypothesis; gender and candidate preference are dependent

3.25

In the following table, likely voters' preferences of two candidates are cross-classified by gender. For the chi-square test of independence, the value of the test statistic is _______. Multiple Choice - 2.34 - 1.62 - 3.25 - 4

reject the null hypothesis; gender and candidate preference are dependent

In the following table, likely voters' preferences of two candidates are cross-classified by gender. Using the critical value approach, the decision and conclusion are ________________________________________. Multiple Choice - reject the null hypothesis; gender and candidate preference are dependent - do not reject the null hypothesis; gender and candidate preference are independent - reject the null hypothesis; gender and candidate preference are independent - do not reject the null hypothesis; gender and candidate preference are dependent

[129.8497, 140.1503]

Professors of accountancy are in high demand at American universities. A random sample of 28 new accounting professors found the average salary was $135 thousand with a standard deviation of $16 thousand. Assume the distribution is normally distributed. Construct a 90% confidence interval for the salary of new accounting professors. Answers are in thousands of dollars. Multiple Choice - [107.7520, 162.2480] - [129.8497, 140.1503] - [130.0260, 139.9740] - [131.0268, 138.9732]

True

T/F: The required sample size for the interval estimation of the population mean can be computed if we specify the population standard deviation σ, the value of zα/2zα/2 based on the confidence level 100(1 − α)% and the desired margin of error E.

[128.7958, 141.2042]

Professors of accountancy are in high demand at American universities. A random sample of 28 new accounting professors found the average salary was $135 thousand with a standard deviation of $16 thousand. Assume the distribution is normally distributed. Construct a 95% confidence interval for the salary of new accounting professors. Answers are in thousands of dollars. Multiple Choice - [102.1680, 167.832] - [127.8247, 142.1753] - [128.7958, 141.2042] - [129.0735, 140.9265]

Independent

Statistical inference about the differences between two population means is based on _________ random samples.

The average debt has not changed.

Students who graduated from college last year owed an average of $25,250 in student loans. An economist wants to determine if average debt has changed. She takes a sample of 40 recent graduates and finds that their average debt is $27,500 with a standard deviation of $9,120. Use 90% confidence interval. Which of the following conclusion is correct? Multiple Choice - The average debt decreased. - The average debt increased. - The average debt has not changed. - There is not enough information.

Do not reject the null hypothesis; we cannot conclude that credit score and income are not independent of one another.

Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. Based on the critical value approach and using α = 0.01, which of the following would be the decision and conclusion for this hypothesis test? Multiple Choice - Reject the null hypothesis; we cannot conclude that credit score and income are independent of one another. - Do not reject the null hypothesis; we can conclude that credit score and income are independent of one another. - Do not reject the null hypothesis; we cannot conclude that credit score and income are not independent of one another. - Reject the null hypothesis; we can conclude that credit score and income are independent of one another.

3.320

Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. The test statistic for this sample is ________. Multiple Choice - 1.766 - 3.320 - 7.051 - 10.576

[$20.46, $24.16]

Suppose taxi fare from Logan Airport to downtown Boston is known to be normally distributed with a standard deviation of $2.50. The last seven times John has taken a taxi from Logan to downtown Boston, the fares have been $22.10, $23.25, $21.35, $24.50, $21.90, $20.75, and $22.65. What is a 95% confidence interval for the population mean taxi fare? Multiple Choice - [$17.46, $27.26] - [$20.46, $24.16] - [$20.80, $23.91] - [$21.66, $23.06]

False

T/F: For a chi-square test of a contingency table, each expected frequency must be at least 3.

True

T/F: For a chi-square test of a contingency table, the degrees of freedom are calculated as (r−1)(c−1) where r and c are the number of rows and columns in the contingency table.

True

T/F: For a chi-square test of a contingency table, the expected frequencies for each cell are calculated assuming the two events are independent of one another.

True

T/F: For a statistical inference regarding μ1−μ2μ1− μ2 , it is imperative that the sampling distribution of X⎯⎯⎯1−X⎯⎯⎯2X¯1-X¯2 is normally distributed.

True

T/F: If a random sample of size n is taken from a normal population with a finite variance, then the statistic T=X⎯⎯⎯ − μS/n√T=X¯ - μS/n follows the tdf distribution with (n − 1) degrees of freedom, df.

True Explanation: The estimate will be less precise if the variability of the underlying population is high or a small segment of the population is sampled.

T/F: If a small segment of the population is sampled then an estimate will be less precise.

False

T/F: If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of X¯1⁢− X¯2 is approximately normal only if the sum of the sample observations is sufficiently large—that is, when n1+n2 ≥30.

True

T/F: In the case when σ21 and σ22 are unknown and can be assumed equal, we can calculate a pooled estimate of the population variance.

False - Because like the z distribution the tdf distribution is symmetic about zero, bell shaped and with tails that approaches to the horizontal axis and never touch it. - Because we know that, In z distribution curve approaches to the horizontal axis but never touch it. - Because range of value in both z and t distribution is - infinity to + infinity.

T/F: Like the z distribution, the tdf distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it.

True

T/F: The chi-square test statistic measures the difference between the observed frequencies and the expected frequencies assuming the null hypothesis is true.

False The confidence interval for the difference in population means is based on the same approach used in the case of one sample: Point Estimate ± Margin of Error.

T/F: The confidence interval for the difference μ1 − μ2 is based on the same approach used in the case of one sample: Point Estimate ± Standard Error.

False The difference between the two sample means X¯1− X¯2⁢ is a point estimator of the difference between two population means μ1− μ2.

T/F: The difference between the two sample means X¯1− X¯2⁢ is an interval estimator of the difference between two population means μ1− μ2 .

True

T/F: The main ingredient for developing a confidence interval is the sampling distribution of the underlying statistic.

1 - α

The confidence coefficient is equal to ________.

6

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. For the chi-square test for independence to be valid, Martha combines the seniorities Manager and Director. As a result, the degrees of freedom used are _____. Multiple Choice - 2 - 16 - 3 - 6

11.293

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. For the chi-square test of independence to be valid, Martha combines the seniorities Manager and Director. The resulting value of the test statistic is _______. Multiple Choice - 12.221 - 11.293 - 17.853 - 20.154

do not reject the null hypothesis; conclude race and seniority are independent

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. For the chi-square test of independence to be valid, Martha combines the seniorities Manager and Director. Using the critical value approach, the decision and conclusion are _______________________________________________________________. Multiple Choice - reject the hypothesis; conclude race and seniority are dependent - reject the null hypothesis; conclude race and seniority are independent - do not reject the null hypothesis; conclude race and seniority are dependent - do not reject the null hypothesis; conclude race and seniority are independent

do not reject the null hypothesis; cannot conclude race and seniority are dependent

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. For the chi-square test of independence to be valid, Martha combines the seniorities Manager and Director. Using the p-value approach and α = 0.05, the decision and conclusion are ________________________________________________________________________. Multiple Choice - reject the null hypothesis; conclude race and seniority are dependent - reject the null hypothesis; conclude race and seniority are independent - do not reject the null hypothesis; cannot conclude race and seniority are dependent - do not reject the null hypothesis; conclude race and seniority are independent

H0: Race and seniority are independent; HA: Race and seniority are dependent

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. To test that race and seniority are independent, the null and alternative hypothesis are _______________________________________________________________________. Multiple Choice - H0: Race and seniority are independent; HA: Race and seniority are dependent - H0: Race and seniority are mutually exclusive; HA: Race and seniority are not mutually exclusive - H0: Race and seniority are not mutually exclusive; HA: Race and seniority are mutually exclusive - H0: Race and seniority are dependent; HA: Race and seniority are independent

reject the null hypothesis; conclude that heights are not normally distributed

The heights (in cm) for a random sample of 60 males were measured. The sample mean is 166.55, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. The following table shows the heights subdivided into non-overlapping intervals. Using the p-value approach and α = 0.05, the decision and conclusion are ___________________________________________________________________. Multiple Choice - reject the null hypothesis; conclude that heights are normally distributed - reject the null hypothesis; conclude that heights are not normally distributed - do not reject the null hypothesis; conclude that heights are normally distributed - do not reject the null hypothesis; conclude that heights are not normally distributed

D = 1.1441

The minimum sample size n required to estimate a population mean with 95% confidence and the assumed estimate of the population standard deviation 6.5 was found to be 124. Which of the following is the approximate value of the assumed desired margin of error? Multiple Choice - D = 0.9220 - D = 0.9602 - D = 1.1441 - D = 1.3090

10.7690

The minimum sample size n required to estimate a population mean with 95% confidence and the desired margin of error 1.5 was found to be 198. Which of the following is the approximate value of the assumed estimate of the population standard deviation? Multiple Choice - 10.7690 - 12.8309 - 115.9671 - 164.6326

[293.2229, 372.2771]

The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S. economy in many ways, but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure and lenders became more wary of filing faulty documentation. Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed, transferring the property) has been 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days. Assume the duration is normally distributed. Construct a 90% confidence interval for the mean duration of the foreclosure process in Boston. Multiple Choice - [259.7400, 405.7600] - [293.2229, 372.2771] - [298.4296, 367.0704] - [303.2282, 362.2718]

[259.7393, 405.7607]

The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S. economy in many ways, but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure, and lenders became more wary of filing faulty documentation. Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed, transferring the property) has been 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days. Assume the duration is normally distributed. Construct a 99% confidence interval for the mean duration of the foreclosure process in Boston. Multiple Choice - [126.2730, 539.2270] - [259.7393, 405.7607] - [279.0056, 386.4944] - [291.8600, 373.6400]

proportion

The parameter p represents the ________ of successes in the population.

normal

To construct a 95% confidence interval for µ, the sampling distribution of X¯ must be _______.

t-test

To use R for solving hypothesis tests for the difference between two means, use the function _________ .