BANA EXAM

The Statistics in Practice example in Chapter 10 identifies an application concerned with: A)inventory evaluation B)food safety C)sales D)new drug testing

D) New Drug Testing

Salary information regarding male and female employees of a large company is shown below. See BANA 10.1 Excel The point estimate of the difference in means is 8 and the margin of error is 5.88. What is the 95% confidence interval for the difference between the means of the two populations? A)−3 to 3 B)−1.96 to 1.96 C)0 to 5.88 D)2.12 to 13.88

D)2.12 to 13.88

The following information was obtained from matched samples taken from two populations. The daily production rates for a sample of workers before and after a training program are shown below. Assume the population of differences is normally distributed. Worker Before After 1 21 24 2 26 25 3 28 29 4 24 22 5 23 27 6 21 21 7 18 20 Given that the null hypothesis to be tested is H0: 𝜇d = 0 at 𝛼 = 0.05, and the test statistic is 1.04,

the null hypothesis should not be rejected.

In hypothesis tests about p1 − p2, what is the pooled estimator of p?

weighted average of p1 and p2.

The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 56 A, 33 B and 31 C responses. What is the relative frequency of C? Round your answer to two decimal places.

0.26

Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on textbooks during the fall semester. The population standard deviations are also shown below. University A University B Sample Size 48 38 Average Purchase $261 $251 Standard Deviation (𝜎) $19 $23 We want to determine if, on the average, students at University A spent more on textbooks than the students at University B. (a)Formulate hypotheses so that, if the null hypothesis is rejected, we can conclude that students at University A spent more than students at University B. A)H0: 𝜇A − 𝜇B ≤ 0 Ha: 𝜇A − 𝜇B > 0 B)H0: 𝜇A − 𝜇B ≥ 0 Ha: 𝜇A − 𝜇B < 0 C)H0: 𝜇A − 𝜇B ≠ 0 Ha: 𝜇A − 𝜇B = 0 D)H0: 𝜇A − 𝜇B > 0 Ha: 𝜇A − 𝜇B = 0 E)H0: 𝜇A − 𝜇B = 0 Ha: 𝜇A − 𝜇B ≠ 0 (b)Compute the test statistic. (Use University A − University B. Round your answer to three decimal places.) (c)Compute the p-value. (Round your answer to three decimal places.) (d)What is your conclusion? Use 𝛼 = 0.02.

(a) A)H0: 𝜇A − 𝜇B ≤ 0 Ha: 𝜇A − 𝜇B > 0 (b) 2.160 (c) .015 (d) Reject H0. We can conclude that students at University A spent more than students at University B.

Babies weighing less than 5.5 pounds at birth are considered "low-birth-weight babies." In the United States, 7.6% of newborns are low-birth-weight babies. The following information was accumulated from samples of new births taken from two counties. Hamilton Shelby Sample Size 159 252 Number of low-weight babies 22 32 (a) Develop a 95% confidence interval estimate for the difference between the proportions of low-birth-weight babies in the two counties. (Use Hamilton − Shelby. Round your answers to four decimal places.) (b) Is there conclusive evidence that one of the proportions is significantly more than the other? If yes, which county? Explain, using the results of part (a). Do not perform any test.

(a) -0.0562 to 0.0790 (b) Because the range of the interval is from negative to positive, there is no indication that one proportion is significantly different (at 95% confidence) from the other.

During recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi. State Voters Surveyed Voters Favoring Dem Alabama 814 439 Mississippi 608 358 We want to determine whether or not the proportions of voters favoring the Democratic candidate were the same in both states. (Use Alabama − Mississippi.) (a) Provide the hypotheses. (b) Compute the test statistic. (Round your answer to three decimal places.) (c) Determine the p-value and, at a 0.05 level of significance, test the above hypotheses.

(a) H0: p1 − p2 = 0 Ha: p1 − p2 ≠ 0 (b) -1.861 (c) We do not reject H0. There is no significant difference.

The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time.com). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars. Private Colleges 52.8 43.2 45.0 33.3 44.0 30.6 45.8 37.8 50.5 42.0 Public Colleges20.3 22.0 28.2 15.6 24.1 28.5 22.8 25.8 18.5 25.6 14.4 21.8 (a) Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.) Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.) (b)What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private − Public.) (c)Develop a 95% confidence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private − Public. Round your answers to one decimal place.)

(a) PRIVATE sample mean $42.5 thousand sample standard deviation $6.98 thousand x1 = xin1 = 42510 = $42.5 thousand s1 = (xi − x1)2n1 − 1 = 438.5610 − 1 = $6.98 thousand PUBLIC sample mean $22.3 thousand sample standard deviation $4.53 thousand x2 = xin2 = 267.612 = $22.3 thousand s2 = (xi − x2)2n2 = 225.9612 − 1 = $4.53 thousand (b) $20.2 thousand Interpret this value in terms of the annual cost (in dollars) of attending private and public colleges. We estimate that the mean annual cost to attend private colleges is $20,200 more than the mean annual cost to attend public college x1 − x2 = 42.5 − 22.3 = 20.2 or $20.2 thousand (c) $14.7 thousand to $25.7 thousand df = s12n1 + s22n22 1n1 − 1s12n12 + 1n2 − 1s22n22 = 6.98210 + 4.532122 196.982102 + 1114.532122 = 14.9 Use df = 14, t0.025 = 2.145. (x1 − x2) ± t0.025s12n1 + s22n220.2±2.1456.98210 + 4.53212 20.2±5.5 ($14.7 thousand to $25.7 thousand)

Hotel room pricing changes over time, but is there a difference between Europe hotel prices and U.S. hotel prices? The file IntHotels contains changes in the hotel prices for 47 major European cities and 53 major U.S. cities.† (a)On the basis of the sample results, can we conclude that the mean change in hotel rates in Europe and the United States are different? Develop appropriate null and alternative hypotheses. (Let 𝜇1 = the population mean change in hotel rates in Europe, and let 𝜇2 = the population mean change in hotel rates in the United States. Enter != for ≠ as needed.) (b)Use 𝛼 = 0.01. Calculate the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) What is your conclusion?

(a) 𝜇1 = the population mean change in hotel rates in Europe 𝜇2 = the population mean change in hotel rates in the United States H0: 𝜇1 − 𝜇2 = 0 Ha: 𝜇1 − 𝜇2 ≠ 0 (b) -1.134 0.2595 Do not reject H0. The mean change in hotel rates in Europe and the United States are not different. x1 − x2 = 0.039 − 0.047 = −0.008 t = (x1 − x2) − 0s12n1 + s22n2 = (0.039 − 0.047) − 00.0301247 + 0.0364253 = −1.134 df = s12n1 + s22n22 1n1 − 1s12n12 + 1n2 − 1s22n22 = 0.0301247 + 0.03642532 147 − 10.03012472 + 153 − 10.03642532 = 97.5 Rounding down, the degrees of freedom = 97. Because this is a two-tailed test, the p-value is two times the lower-tail area. Using a t table, the area in the lower tail is between 0.10 and 0.20; therefore, the p-value is between 0.20 and 0.40. Using software, p-value = 0.2595. Because the p-value > 0.01, do not reject H0. Conclusion: The mean change in hotel rates in Europe and the United States are not different.

Maxforce, Inc., manufactures racquetball racquets by two different manufacturing processes (A and B). Because the management of this company is interested in estimating the difference between the average time it takes each process to produce a racquet, they selected independent samples from each process. The results of the samples and the population variances are shown below. Process A Process B Sample Size 27 32 Sample Mean (in minutes) 48 54 Population Variance (𝜎2) 65 72 (a)Develop a 95% confidence interval estimate for the difference between the average time taken by the two processes. (Use Process A − Process B. Round your answers to three decimal places.) (b)Is there conclusive evidence to prove that one process takes longer than the other? If yes, which process? Explain.

(a) -10.230 to -1.770 (b) Because the range of the interval is from negative to negative, it indicates that there is conclusive evidence (at 95% confidence) that Process B takes longer.

Of 146 Chattanooga residents surveyed, 53 indicated that they participated in a recycling program. In Knoxville, 112 residents were surveyed and 32 claimed to recycle. (a) Determine a 95% confidence interval estimate for the difference between the proportion of residents recycling in the two cities. (Use Chattanooga − Knoxville. Round your answer to three decimal places.) (b) From your answer in part (a), is there sufficient evidence to conclude that there is a significant difference in the population proportion of residents participating in the recycling program?

(a)-0.037 to 0.192 (b)Because the range of the interval is from negative to positive, it indicates that there is no conclusive evidence (at 95% confidence) that the proportion of Chattanooga residents that recycle is significantly different from Knoxville residents.

Consider the following hypothesis test. H0: 𝜇1 − 𝜇2 = 0 Ha: 𝜇1 − 𝜇2 ≠ 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1 = 80 n2 = 70 x1 = 104 x2 = 106 𝜎1 = 8.4 𝜎2 = 7.2 (a)What is the value of the test statistic? (Round your answer to two decimal places.) (b)What is the p-value? (Round your answer to four decimal places.) (c)With 𝛼 = 0.05, what is your hypothesis testing conclusion?

(a)-1.57 (b)0.1164 (c)Do not reject H0. There is insufficient evidence to conclude that 𝜇1 − 𝜇2 ≠ 0. EXPLANATION (a) z = (x1 − x2) − D0𝜎12n1 + 𝜎22n2 = (104 − 106) − 0(8.4)280 + (7.2)270 = −1.57 (b) p-value = 2(0.0582) = 0.1164 (c) Do not reject H0. There is insufficient evidence to conclude that 𝜇1 − 𝜇2 ≠ 0.

Consider the following results for two samples randomly taken from two normal populations. Sample I Sample II Sample Size 24 33 Sample Mean 47 43 Population I Population II Standard Deviation 13 13 (a)Develop a 90% confidence interval for the difference between the two population means. (Use Sample I − Sample II. Round your answers to three decimal places.) (b)Is there conclusive evidence that one population has a larger mean? Explain.

(a)-1.736 to 9.736 (b)Because the range of the interval is from negative to positive, it indicates that there is no conclusive evidence (at 90% confidence) that one population has a larger mean.

In a sample of 108 Republicans, 66 favored the President's anti-drug program. While in a sample of 154 Democrats, 89 favored his program. At 𝛼 = 0.05, test to see if there is a significant difference in the proportions of the Democrats and the Republicans who favored the President's anti-drug program. (Use Republicans − Democrats.) (a) Compute the test statistic. (Round your answer to four decimal places.) (b) What do you conclude?

(a)0.5380 (b)We do not reject H0. There is no significant difference.

Of 305 female registered voters surveyed, 122 indicated they were planning to vote for the incumbent president. Of 405 male registered voters, 146 indicated they were planning to vote for the incumbent president. (a) Compute the test statistic. (Use female − male. Round your answer to three decimal places.) (b) At 𝛼 = 0.01, test to see if there is a significant difference between the population proportions of females and males who plan to vote for the incumbent president. (Use the p-value approach.) Calculate the p-value. (Round your answer to three decimal places.)

(a)1.075 (b)0.282 Do not reject H0. We cannot conclude that there is a significant difference between the two population proportions.

Consider the following hypothesis test. H0: 𝜇1 − 𝜇2 ≤ 0 Ha: 𝜇1 − 𝜇2 > 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1 = 40 n2 = 50 x1 = 25.1 x2 = 22.8 𝜎1 = 5.9 𝜎2 = 6 (a)What is the value of the test statistic? (Round your answer to two decimal places.) (b)What is the p-value? (Round your answer to four decimal places.) (c)With 𝛼 = 0.05, what is your hypothesis testing conclusion?

(a)1.82 (b)0.0341 (c)Reject H0. There is sufficient evidence to conclude that 𝜇1 − 𝜇2 > 0. Note: (a) z = (x1 − x2) − D0𝜎12n1 + 𝜎22n2 = (25.1 − 22.8) − 0(5.9)240 + 6250 = 1.82 (b) p-value = 1.0000 − 0.9659 = 0.0341 (c) Reject H0. There is sufficient evidence to conclude that 𝜇1 − 𝜇2 > 0.

The following results come from two independent random samples taken of two populations. Sample 1Sample 2n1 = 50n2 = 25x1 = 13.6x2 = 11.6𝜎1 = 2.3𝜎2 = 3 (a)What is the point estimate of the difference between the two population means? (Use x1 − x2.) (b)Provide a 90% confidence interval for the difference between the two population means. (Use x1 − x2. Round your answers to two decimal places.) (c)Provide a 95% confidence interval for the difference between the two population means. (Use x1 − x2. Round your answers to two decimal places.)

(a)2 (b)0.88 to 3.12 (c)0.66 to 3.34 EXPLANATION (a)x1 − x2 = 13.6 − 11.6 = 2 (b)z𝛼/2 = z0.05 = 1.645 x1 − x2±1.645𝜎12n1 + 𝜎22n2 2±1.645(2.3)250 + (3)225 2 ± 1.12 (0.88 to 3.12) (c)z𝛼/2 = z0.025 = 1.96 2 ± 1.96(2.3)250 + (3)2252±1.34 (0.66 to 3.34)

The following results are for independent random samples taken from two populations. Sample 1 Sample 2 n1 = 20 n2 = 30 x1 = 22.8 x2 = 20.1 s1 = 2.4 s2 = 4.4 (a)What is the point estimate of the difference between the two population means? (Use x1 − x2.) (b)What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.) (c)At 95% confidence, what is the margin of error? (Round your answer to one decimal place.) (d)What is the 95% confidence interval for the difference between the two population means? (Use x1 − x2. Round your answers to one decimal place.)

(a)2.7 (b)46 (c)1.9 (d)0.8 to 4.6 (a)x1 − x2 = 22.8 − 20.1 = 2.7 (b)df = s12n1 + s22n22 1n1 − 1s12n12 + 1n2 − 1s22n22 = 2.4220 + 4.42302 1192.42202 + 1294.42302 = 46.5 Use df = 46. (c) t0.025 = 2.013 t0.025s12n1 + s22n2 = 2.0132.4220 + 4.4230 = 1.9 (d) 2.7 ± 1.9 (0.8 to 4.6)

A newspaper reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $135.67, and the average expenditure in a sample survey of 30 female consumers was $61.64. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $20. (a)What is the point estimate (in dollars) of the difference between the population mean expenditure for males and the population mean expenditure for females? (Use male − female.) (b)At 99% confidence, what is the margin of error (in dollars)? (Round your answer to the nearest cent.) (c)Develop a 99% confidence interval (in dollars) for the difference between the two population means. (Use male − female. Round your answer to the nearest cent.)

(a)74.03 (b)17.08 (c)56.95 to 91.11 Note: (a) x1 − x2 = 135.67 − 61.64 = $74.03 (b) z𝛼/2𝜎12n1 + 𝜎22n2 = 2.576(35)240 + (20)230 = 17.08 (c) 74.03 ± 17.08 ($56.95 to $91.11) We estimate that men spend $74.03 more than women on Valentine's Day with a margin of error of $17.08.

A consumer product testing organization uses a survey of readers to obtain customer satisfaction ratings for the nation's largest supermarkets. Each survey respondent is asked to rate a specified supermarket based on a variety of factors such as: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all factors. Suppose sample data representative of independent samples of two supermarkets' customers are shown below. Supermarket 1 Supermarket 2 n1 = 260 n2 = 300 x1 = 82 x2 = 81 (a)Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers. (Let 𝜇1 = the population mean satisfaction score for Supermarket 1's customers, and let 𝜇2 = the population mean satisfaction score for Supermarket 2's customers. Enter != for ≠ as needed.) (b)Assume that experience with the satisfaction rating scale indicates that a population standard deviation of 13 is a reasonable assumption for both retailers. Conduct the hypothesis test. Calculate the test statistic. (Use 𝜇1 − 𝜇2. Round your answer to two decimal places.) Report the p-value. (Round your answer to four decimal places.) At a 0.05 level of significance what is your conclusion? (c)Which retailer, if either, appears to have the greater customer satisfaction? Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Use x1 − x2. Round your answers to two decimal places.)

(a)H0: 𝜇1 − 𝜇2 = 0 Ha: 𝜇1 − 𝜇2 ≠ 0 (b) 0.91 p-value = 0.3640 Do not reject H0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. (c)neither -1.16 to 3.16 (a) 𝜇1 = population mean satisfaction score for Supermarket 1's customers 𝜇2 = population mean satisfaction score for Supermarket 2's customers H0: 𝜇1 − 𝜇2 = 0 Ha: 𝜇1 − 𝜇2 ≠ 0 (b) x1 − x2 = 82 − 81 = 1 z = (x1 − x2) − D0𝜎12n1 + 𝜎22n2 = (82 − 81) − 0132260 + 132300 = 0.91 For this two-tailed test, p-value is two times the upper-tail area at z = 0.91. p-value = 2(1.0000 − 0.8180) = 0.3640 p-value > 0.05; do not reject H0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. (c) x1 − x2 ± z0.025𝜎12n1 + 𝜎22n2 (82 − 81) ± 1.96132260 + 132300 1 ± 2.16, −1.16 to 3.16 Because the 95% confidence interval contains zero, the difference between the mean customer satisfaction score of the two supermarkets is not statistically significant at the 95% confidence level.

Given that z is a standard normal random variable, find z if the area to the left of z is 0.3192. (Round your answers to 3 decimal places. .)

-.470

The average home in the U.S. is expected to cost $236,000. A random sample of 58 homes sold this month showed an average price of $223,000 with a sample standard deviation $37,000. We are interested in determining if the cost of the average home has decreased this month. What is the value of the test statistic? (Round your answer to three decimal places.)

-2.676

Based on the information in Question 2 and with 19.48 degrees of freedom, the lower limit of the 95% confidence interval for the difference between the two population means is(Round the answer to three decimal places)

-5.372

Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 14 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. A sample of 35 surveys from a particular client provided the survey times shown in the file named Fowle. Based upon past studies, the population standard deviation is assumed known with σ = 8 minutes. Fowle would like to test whether the premium rate is justified for this customer. What is the p-value associated with this hypothesis test? (Round your answer to three decimal places.)

.013

The average home in the U.S. is expected to cost $240,000. A random sample of 60 homes sold this month showed an average price of $232,000. Assume that you have access to this data. We are interested in determining if the cost of the average home has decreased this month. If the test statistic is -1.72, what is the p-value? (Round your answer to three decimal places.)

.045

Assume you have applied for two jobs Job A and Job B. The probability that you get an offer for only Job A is 0.25. The probability of being offered only Job B is 0.16. The probability of getting at least one of the jobs is 0.36. What is the probability that you will be offered both jobs? (Round your answer to two decimal places.)

.05

Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 35 employees; the Hawaii plant has 25. A random sample of 10 employees is to be asked to fill out a benefits questionnaire. What is the probability that 5 of the employees in the sample work at the plant in Hawaii? (Round your answers to three decimal places.)

.229

According to a 2018 survey by Bankrate.com, 20% of adults in the United States save nothing for retirement (CNBC website). Suppose that twenty-two adults in the United States are selected randomly. What is the probability that more than five of the selected adults save nothing for retirement? (Round your answer to three decimal places.)

.267

The assembly time for a product is uniformly distributed between 10 to 20 minutes. What is the probability that the assembly will take less than 13.2 minutes? (Round you answer to two decimal places.)

.32

If A and B are independent events with P(A) = 0.25 and P(B) = 0.17, then P(A union B) =(Round your answer to two decimal places.)

.38

In a local university, 67% of the students live in the dormitories. A random sample of 78 students is selected for a particular study. We know that the standard error of the proportion is 0.0532. Find the probability that the sample proportion (the proportion living in the dormitories) is between 64% and 70%. (Round your answer to three decimal places.)

.427

A population has a standard deviation of 17. If a sample of size 33 is selected from this population, what is the probability that the sample mean will be within plus or minus two of the population mean? (Round your answer to three decimal places.)

.501

Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUs as efficiently as possible in a hospital. Suppose that a large-scale study of elderly ICU patients shows that the average length of stay in the ICU is 4.9 days. Assume that this length of stay in the ICU has an exponential distribution. What is the probability that the length of stay in the ICU is four days or less? (Round your answer to four decimal places.)

.5579

A life insurance company has determined that each week an average of twelve claims is filed in its Nashville branch. What is the probability that during the next week twelve claims or less will be filed? (Assume that the arrival of claims can be described by a Poisson distribution and round your answer to three decimal places.)

.576

Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm).† Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.7 cm. What is the probability that a Dutch male is between 174 and 192 cm? (Round your answer to three decimal places.)

.600

Compute the probability that z, a standard normal variable, is less than or equal to 1.6. (Round your answer to 4 decimal places.)

.9452

The following information was obtained from matched samples taken from two populations. The daily production rates for a sample of workers before and after a training program are shown below. Assume the population of differences is normally distributed. Worker Before After 1 21 23 2 26 24 3 28 28 4 24 21 5 23 26 6 21 20 7 18 19 The point estimate for the difference between the two population means is 0. The null hypothesis to be tested is H0: 𝜇d = 0. Find the test statistic.

0

Decide whether each situation demonstrates a discrete or continuous random variable. 1. The number of faculty members who entered Lindner yesterday. 2. Your weight in kilograms. 3. The number of times that you have signed into Canvas today. 4. The number of students who attend a recitation session. 5. The amount of time yesterday each student studied for this exam.

1. Discrete 2.Continuous 3. Discrete 4. Discrete 5. Continuous

Use the attached Student Data and an Excel PivotTable to determine the total number of Facebook Friends Finance students have. See TestDataSheet2020

14520

A psychologist developed a new test of adult intelligence. The test was administered to 20 individuals, and the following data were obtained. 124 109 141 134 127 111 115 137 129 125 108 113 154 164 142 115 135 132 128 128 If you construct a stem-and-leaf display for the data, using a leaf unit of 1, the second stem would be

11

The following represents the probability distribution for the daily demand of computers at a local store. Demand Probability 0 0.05 1 0.25 2 0.3 3 0.25 4 0.15 What is the expected daily demand? (Round your answer to two decimal places.)

2.20

The following information was obtained from matched samples taken from two populations. The daily production rates for a sample of workers before and after a training program are shown below. Assume the population of differences is normally distributed. Worker Before After 1 19 23 2 24 24 3 26 28 4 22 21 5 21 26 6 19 20 7 16 19 Find the point estimate for the difference between the population means for the rates after the program and before the program.

2

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed. Driver Manufacturer A Manufacturer B 1 31 27 2 26 21 3 25 26 4 25 23 5 24 23 6 28 24 7 30 27 8 24 26 Find the mean of the differences.

2

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed. The mean of the differences is 3. Find the test statistic.

2.316

Using the attached Student Data, determine the 65th percentile of Facebook Friends. Enter your answer rounded to one decimal place. See TestDataSheet2020

200.0

The following information was obtained from independent random samples taken of two populations. Assume that the populations are normally distributed. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 The point estimate for the difference between the mean of population 1 and the mean of population 2 is(Round the answer to the nearest whole number.)

3

Based on the information in Question 1, the standard error of the difference in the means is(Round the answer to two decimal places)

4

Using the attached Student Data, determine the skewness of Facebook Friends in this sample. Enter your answer rounded to one decimal place. Consider this data a sample not a population. See TestDataFall2020

3.2

The file HongKongMeals contains the costs for a sample of 42 recent meals for two in Hong Kong midrange restaurants. What is the 94% confidence interval estimate of the population mean cost in dollars for a mid-range meal for two in Hong Kong? (Round your answers to the nearest cent.)

30.62 to 34.70

Using the attached Student Data, determine the median of Sleep. Enter your answer rounded to one decimal places. See TestDataSheet2020

465

Using the attached Student Data, determine the 3rd quartile of Sleep. Enter your answer rounded to one decimal place. See TestDataSheet2020

480

Suppose that, from a population of sixty bank accounts, we want to take a random sample of five accounts in order to learn about the population. How many different random samples of five accounts are possible?

5,461,512

The student body of a large university consists of 57% Arts & Science students. A random sample of 10 students is selected. What is the expected number of Arts & Science students selected? (Round your answer to one decimal place.)

5.7

An experiment consists of three steps. There are two possible results on the first step, fourteen possible results on the second step, and nineteen possible results on the third step. The total number of experimental outcomes is

532

Using the attached Student Data, determine the average of Sleep. Enter your answer rounded to one decimal place. See TestDataSheet2020

555.9

A population has a standard deviation of 36. A random sample of 133 items from this population is selected. The sample mean is determined to be 325. What is the margin of error at 95% confidence? (Round your answer to three decimals.)

6.118

A simple random sample of 80 items resulted in a sample mean of 65. The population standard deviation is 𝜎 = 10.Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.)

62.81 to 67.19

Use the attached Student Data and an Excel PivotTable to determine the number of students who are Marketing majors and do not wear contacts or glasses. See TestDataSheet2020

82

The company identified in Chapter 10, Statistics in Practice is: A)U.S. Food & Drug Administration B)John Morrell & Company C)MeadWestvaco Corporation D)Food Lion

A) U.S. Food & Drug Administration

Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 68 32 Sample Mean Salary(in $1,000s) 55 52 Population Variance (𝜎2) 136 64 The test statistic is 1.5. In a test of whether or not the population average salary of males is significantly greater than that of females, what is the p-value? A)0.0668 B)0.1336 C)0.8664 D)0.9332

A)0.0668

The sum of the probabilities of two complementary events is A)1.0 B)0 C)unknown D)0.50

A)1.0

If you created a bar chart showing the frequency of Birth Month using the attached Student Data, the month with the lowest bar would be See TestDataSheet2020 A)August B)October C)April D)February E)January

A)August

For a given level of Type I error, if we want to decrease the level of Type II error, the sample size must A)increase B)remain the same C)decrease D)increase or decrease since it has no impact on Type II error.

A)increase

Consider the attached Student Data. Major is an example of a variable that uses the A)nominal scale B)interval scale C)ratio scale D)ordinal scale

A)nominal scale

A random sample of 100 people was taken. Eighty-one of the people in the sample favored Candidate A. We are interested in determining whether the proportion of the population in favor of Candidate A is significantly more than 79%. We know that the p-value is 0.3117. At the 0.05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is A)not significantly greater than 79%. B)not significantly greater than 81%. C)significantly greater than 81%. D)significantly greater than 79%

A)not significantly greater than 79%.

The key difference between the binomial and hypergeometric distributions is that, with the hypergeometric distribution, the A)probability of success changes from trial to trial. B)trials are independent of each other. C)probability of success must be less than 0.5. D)random variable is continuous.

A)probability of success changes from trial to trial.

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. Company A Company B Sample size 70 55 Sample mean $15.75 $15.25 Sample standard deviation $1.00 $0.95 The p-value is 0.0052. At the 5% level of significance, the null hypothesis A)should be rejected. B)should not be rejected. C)should not be tested. D)should be revised.

A)should be rejected.

Bayes' theorem is used to compute A)the posterior probabilities B)the prior probabilities C)the union of events D)intersection of events

A)the posterior probabilities

In computing the standard error of the mean, the finite population correction factor is used when A)the sample size compared to the population size is greater than 5%. B)the sample size is less than thirty. C)the sample size is thirty or greater. D)the sample size compared to the population size is less than 5%.

A)the sample size compared to the population size is greater than 5%.

Since a sample is a subset of the population, the sample mean _____ the mean of the population. A)varies around B)is always larger than C)must be equal to D)is always smaller than

A)varies around

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. Company A Company B Sample size 70 45 Sample mean $14.75 $14.35 Sample standard deviation $1.00 $0.95 The test statistic is 2.16 with 97 degrees of freedom. Find the p-value. A)0.0166 B)0.0332 C)0.0665 D)0.9668

B)0.0332

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. Company A Company B Sample size 70 45 Sample mean $17.75 $16.25 Sample standard deviation $1.00 $0.95 Find a point estimate for the difference between the two population means. A)0.05 B)1.50 C)2.00 D)25.00

B)1.50

Salary information regarding male and female employees of a large company is shown below. See BANA 10.1 Excel Find the standard error of the difference between the two sample means. A)2.89 B)3 C)9 D)19.52

B)3

Salary information regarding male and female employees of a large company is shown below. See BANA 10.1 Excel The standard error is 2. What is the margin of error at 95% confidence? A)1.960 B)3.920 C)3.960 D)7.840

B)3.920

Salary information regarding male and female employees of a large company is shown below. See BANA 10.1 Excel Find the point estimate of the difference between the means of the two populations. A)6 B)7 C)24 D)72

B)7

As the sample size becomes larger, the sampling distribution of the sample mean approaches a(n) A)Binomial distribution B)Normal distribution C)Exponential distribution D)Poisson distribution

B)Normal distribution

A graphical presentation of the relationship between two variables is A)a stem and leaf display B)a scatter diagram C)a dot plot D)a histogram

B)a scatter diagram

A seven-year medical research study reported that women whose mothers took the drug diethylstilbestrol (DES) during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug. This study compared two populations. What were the populations? (Select all that apply.) A)women participating in the research study whose mothers took the drug DES during pregnancy B)all women whose mothers did not take the drug DES during pregnancy C)women participating in the research who did develop tissue abnormalities that might lead to cancer D)women participating in the research study whose mothers did not take the drug DES during pregnancy E)all women who did not develop tissue abnormalities that might lead to cancer F)all women whose mothers took the drug DES during pregnancy

B)all women whose mothers did not take the drug DES during pregnancy F)all women whose mothers took the drug DES during pregnancy

If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means: A)will have a mean of one B)can be approximated by a normal distribution C)can be approximated by any distribution D)will have a variance of one

B)can be approximated by a normal distribution

If the level of significance of a hypothesis test is raised from 0.05 to 0.2, the probability of a Type II error will A)decrease. B)increase. C)not change. D)also increase from 0.05 to 0.2.

B)increase.

For a sample of retired teachers, several health factors are collected and compared for teachers who worked in older schools with asbestos issues and for teachers who worked in newer schools without asbestos issues This study would be considered A)experimental B)observational C)both observational and experimental D)neither observational nor experimental

B)observational

What will the sum of the relative frequencies for all classes always equal? A)100 B)one C)the sample size D)any value larger than one

B)one

To decrease the margin of error, the sample size A)could increase or decrease since it has no impact on the margin of error. B)should increase. C)should increase or decrease depending on the value of the mean. D)should decrease.

B)should increase.

One hundred graduating LCB students are randomly selected to participate in a survey. The survey asks many questions including whether the students plan to attend graduate school. LCB will use this data to highlight the percentage of graduating LCB students who plan to attend graduate school. Using the sample percentage to estimate the percentage of graduating LCB students who plan to attend graduate school is an example of A)a sample B)statistical inference C)prescriptive analytics D)descriptive statistics

B)statistical inference

Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 68 34 Sample Mean Salary(in $1,000s) 58 51 Population Variance (𝜎2) 272 170 In a test of whether or not the population average salary of males is significantly greater than that of females at 𝛼 = 0.05, the p-value is 0.0098. The conclusion is that A)the population salaries of males and females are equal. B)the population average salary of males is significantly greater than that of females. C)the population average salary of males is significantly lower than that of females. D)there is no evidence that the population average salary of males is greater than that of females.

B)the population average salary of males is significantly greater than that of females.

Chapter 10's primary focus is: A)regression analysis B)descriptive statistics C)hypothesis testing with one population D)hypothesis testing with two populations

D) Hypothesis testing with two populations

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. Company A Company B Sample size 85 40 Sample mean $17.75 $17.25 Sample standard deviation $1.00 $0.95 The point estimate for the difference between the two population means is 0.5. Find the test statistic. A)0.19 B)1.85 C)2.70 D)3.82

C)2.70

The average manufacturing workweek in metropolitan Chattanooga was 40.1 hours last year. It is believed that the contracting economy has led to a decrease in the average workweek. To test the validity of this belief, the hypotheses are A)H₀: the population mean is less than or equal to 40.1; Hᴀ: the population mean is greater than 40.1 B)H₀: the population mean is greater than 40.1; Hᴀ: the population mean is less than or equal to 40.1 C)H₀: the population mean is greater than or equal to 40.1; Hᴀ: the population mean is less than 40.1 D)H₀: the population mean equals 40.1; Hᴀ: the population mean is not equal to 40.1

C)H₀: the population mean is greater than or equal to 40.1; Hᴀ: the population mean is less than 40.1

If a hypothesis test leads to the rejection of the null hypothesis, A)a Type II error may have been committed B)a Type I error must have been committed C)a Type I error may have been committed D)a Type II error must have been committed

C)a Type I error may have been committed

A box plot is a graphical representation of data that is based on A)a histogram B)z-scores C)a five number summary D)the empirical rule.

C)a five number summary

The probability that a continuous random variable takes any specific value A)is very close to 1.0 B)is at least 0.5 C)is equal to zero D)depends on the probability density function

C)is equal to zero

The purpose of statistical inference is to provide information about the A)population based upon information contained in the population. B)sample based upon information contained in the population. C)population based upon information contained in the sample. D)mean of the sample based upon the mean of the population.

C)population based upon information contained in the sample.

The average home in the U.S. is expected to cost $240,000. A random sample of homes sold this month showed an average price of $232,000. We are interested in determining if the cost of the average home has decreased this month. If the p-value associated with the test statistic is less than .001, our conclusion would be A)the cost of the average house is equal to $240,000. B)the cost of the average house is less than or equal to $240,000. C)the cost of the average house is less than $240,000. D)the cost of the average house is greater than or equal to $240,000

C)the cost of the average house is less than $240,000.

Which of the following is the interquartile range? A)the 50th percentile B)another name for the standard deviation C)the difference between the third quartile and the first quartile D)the difference between the largest and smallest values

C)the difference between the third quartile and the first quartile

Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 68 34 Sample Mean Salary(in $1,000s) 61 52 Population Variance (𝜎2) 272 170 The point estimate of the difference in means is 9 and the standard error is 3. In a test of whether or not the population average salary of males is significantly greater than that of females at 𝛼 = 0.05, what is the test statistic? A)1.5 B)1.645 C)1.96 D)3

D)3

In cluster sampling, A)randomly selected elements within the randomly selected clusters form the sample. B)randomly selected elements within each of the clusters form the sample. C)all elements within each of the clusters form the sample. D)all elements within the randomly selected clusters form the sample.

D)all elements within the randomly selected clusters form the sample.

The intersection of two mutually exclusive events A)must always be equal to 1. B)can be any value between 0 to 1. C)can be any positive value. D)must always be equal to 0.

D)must always be equal to 0.

Consider the attached Student Data. Height is an example of a variable that uses the A)ordinal scale B)nominal scale C)interval scale D)ratio scale

D)ratio scale

In hypothesis testing, the tentative assumption about the population parameter is A)None of these alternatives is correct B)either the null or the alternative C)the alternative hypothesis D)the null hypothesis

D)the null hypothesis

Scores were gathered for the first round and the last round for the same twenty golfers at a recent tournament. Consider the attached output. What is the appropriate conclusion?

The scores are higher in the final round but the difference is not statistically significant.

Of the two production methods, a company wants to identify the method with the smaller population mean completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on

matched samples.

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.

matched, independent

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as _____ samples.

matched

The sampling distribution of p1 − p2 is approximated by a normal distribution if _____ are all greater than or equal to 5.

n1p1, n1(1 − p1), n2p2, n2(1 − p2)

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n₁ = 500 n₂ = 600 Number of Accidents = 180 Number of Accidents = 150 We are interested in determining if the accident proportions differ between the two age groups.Let pu represent the proportion under and p₀ the proportion over the age of 18. The null hypothesis is

pu - p₀ is equal to zero

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed. The test statistic is 2.316. At 𝛼 = 0.10, the null hypothesis

should be rejected.