College Board Unit 7 HW

A university researcher wants to estimate the mean number of novels that seniors read during their time in college. An exit survey was conducted with a random sample of 9 seniors. The sample mean was 7 novels with standard deviation 2.29 novels. Assuming that all conditions for conducting inference have been met, which of the following is a 95 percent confidence interval for the population mean number of novels read by all seniors? Go to image for answers

The point estimate is 7. The standard error is the sample standard deviation 2.29 divided by the square root of the sample size 9. There are n-1 = 9-1 = 8 degrees of freedom, and the correct value of t is 2.306

A marine biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate. Which of the following is an appropriate method for the biologist to use for inference to the population? A: A one-sample t-interval for a population mean B: A one-sample t-interval for a sample mean C: A one-sample z-interval for a population proportion D: A matched-pairs t-interval for a mean difference E: A two-sample t-interval for a difference between means

A: A one-sample t-interval for a population mean Weight is a quantitative variable. The appropriate procedure for estimation is the one-sample t-interval for a population mean

A business analyst is investigating whether the mean amount of purchases made by customers at an online department store is greater than $100. The analyst obtained a random sample of 56 orders and calculated a sample mean of $102.30 and a sample standard deviation of $5.30. Which of the following is an appropriate test for the investigation? A: A one-sample t-test for a population mean B: A one-sample t-test for a sample mean C: A one-sample z-test for a population proportion D: A two-sample t-test for a difference between population means E: A matched-pairs t-test for a mean difference

A: A one-sample t-test for a population mean Because the population standard deviation is unknown and the sample standard deviation will be used, a t-test is appropriate

A study will conducted to investigate whether there is a difference in mean tail lengths between two populations of snow leopards. Random samples of leopards will be selected from both populations, and the mean sample tail length will be calculated for each sample. Which of the following is the appropriate test for the study? A: A two-sample t-test for a difference between population means B: A two-sample z-test for a difference between population proportions C: A one-sample z-test for a population proportion D: A one-sample t-test for a sample mean E: A one-sample t-test for a population mean

A: A two-sample t-test for a difference between population means Two random samples will be selected on a quantitative variable, and the difference in the sample means will be calculated. The appropriate test is the two-sample t-test for a difference in means

A fast-food restaurant claims that a small order of french fries contains 120 cal. A nutritionist is concerned that the true average cal count is higher than that. The nutritionist randomly selects 35 small orders of french fries and determines their cal. The resulting x̄ is 155.6 cal, and the p-value for the HT is 0.00093. Which of the following is the correct interpretation of the p-value? A: If the μ is 120 cal, the p-value of 0.00093 is the prob. of observing a x̄ of 155.6 cal or more B: If the μ is 120 cal, the p-value of 0.00093 is the prob. of observing a x̄ of 155.6 cal or less C: If the μ is 120 cal, the p-value of 0.00093 is the prob. of observing a x̄ of 155.6 cal or more, or a x̄ of 84.4 cal or less D: If the μ is 155.6 cal, the p-value of 0.00093 is the prob. of observing a x̄ of 120 cal or more E: If the μ is 155.6 cal, the p-value of 0.00093 is the prob. of observing a x̄ of 120 cal or

A: If the population mean is 120 calories, the p-value of 0.00093 is the probability of observing a sample mean of 155.6 calories or more If the null hypothesis is true, the p-value is the probability of observing the sample mean (155.6) or more

Researchers are investigating the effectiveness of leg-strength training on cycling performance. A sample of 7 men will be selected to participate in a training program that lasts for one month. Peak power during cycling will be recorded for each man both before training and after training. The mean difference in times will be used to construct a 95% CI for the mean difference in the population. When all other things remain the same, which of the following statements about the width of the interval is correct? A: The interval will be narrower if 15 men are used in the sample B: The interval will be wider if 15 men are used in the sample C: The interval will be narrower if 5 men are used in the sample D: The interval will be narrower if the level is increased to 99% confidence E: The interval will be wider if the level is decreased to 90% confidence

A: The interval will be narrower if 15 men are used in the sample When all other things remain the same, the width of a confidence interval will decrease as the sample size increases (from n = 7 to n = 15)

Which of the following statements correctly explains what happens to the variability of a t-distribution as the sample size increases? A: The variability of the t-distribution decreases as the sample size increases because the sample standard deviation approaches the population standard deviation B: The variability of the t-distribution increases as the sample size increases because the sample standard deviation approaches the population standard deviation C: The variability of the t-distribution increases as the sample size increases because the mean of the distribution increases D: The variability of the t-distribution decreases as the sample size increases because the mean of the distribution decreases E: The variability of the t-distribution remains constant as the sample size increases because the t-statistic is defined by the sample standard deviation

A: The variability of the t-distribution decreases as the sample size increases because the sample standard deviation approaches the population standard deviation As sample size increases, s approaches σ, and the t-distribution approaches the z-distribution. There are more observations closer to the center of a z-distribution than in any t-distribution, so the variability in a t-distribution decreases as the sample size increases because the t-distribution approaches a z-distribution

To investigate hospital costs for pets in a certain state, researchers selected a RS of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner (PO) was recorded and used to create the 95% CI $62.63 ± $17.64. Assuming all conditions, which of the following is a correct interpretation of the interval? A: We are 95% conf. that the mean cost of a HV for all PO in the state is between $44.99 and $80.27 B: We are 95% conf. that the mean cost of a HV for the PO in the sample is between $44.99 and $80.27 C: For all PO in the state, 95% of a HV for parrot care cost between $44.99 and $80.27 D: There is a 0.95 prob. that the mean cost of a HV for all PO in the state is between $44.99 and $80.27 E: There is a 0.95 prob. that the mean cost of a HV for the PO in the sample is between $44.99 and $80.27

A: We are 95% confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27 The percent is how much confidence exists that the interval has captured the population mean

For a t-distribution with sample size 10, P(t ≥ 1.96) ~ 0.0408 and P(t ≤ -1.96) ~ 0.0408. Which of the following is a property of the t-distribution illustrated by the probabilities? A: With sample size 10, the tails of the curve of the t-distribution have more area than the tails of the curve of the z-distribution B: With sample size 10, the tails of the curve of the t-distribution have less area than the tails of the curve of the z-distribution C: With sample size 10, the middle of the curve of the t-distribution has more area than the middle of the curve of the z-distribution D: With sample size 10, the mean of the t-distribution is greater than the mean of the z-distribution E: With sample size 10, the mean of the t-distribution is less than the mean of the z-distribution

A: With sample size 10, the tails of the curve of the t-distribution have more area than the tails of the curve of the z-distribution The area under the z-curve is 0.025 to the right of 1.96 and to the left of -1.96. Because 0.0408 is greater than 0.025, we can conclude that the t-curve has more area in its tails

A two-sample t-test for a difference in means will be conducted to investigate mean gasoline prices in two states. From each state, 45 gasoline stations will be selected at random. On the same day, the price o regular gasoline will be recorded for each selected station and the sample mean price for each state will be calculated. Have all conditions for inference been met? A: Yes, all conditions have been met B: No, the data are not collected using a random method C: No, the sample sizes are greater than 10 percent of the population D: No, the sample sizes are not large enough to assume the sampling distribution is approximately normal E: No, the distributions of the sample data are not approximately normal

A: Yes, all conditions have been met The data are being collected using a random method. The sample sizes are large enough (both 45) to support the assumption of normality for the sampling distribution of the difference in sample means. Also, it is reasonable to assume that 45 gasoline stations is less than 10 percent of all the gas stations in each state

A recent study reported the mean body mass index (BMI) for adults in the United States was 26.8. A researcher believes the mean BMI of marathon runners is less than 26.8. A random sample of 35 marathon runners had a mean BMI of 22.7 with a standard deviation of 3.1. The researcher will conduct a one-sample t-test for a population mean. Have the conditions for inference been met? A: Yes, all conditions have been met B: No, because the sample was not selected using a random method C: No, because marathon runners are not a representative sample of all adults in the United States D: No, because the shape of the distribution of the sample is not known E: No, because the sample size is not large enough to assume normality of the sampling distribution of the sample mean

A: Yes, all conditions have been met The independence condition was met because the marathon runners were selected randomly, and 35 runners is less than 10% of all marathon runners. Also, the sample size of 35 is large enough to assume that the distribution of sample means is approximately normal

Researchers investigated whether there is a difference between two headache meds, R and S. Researchers measured the mean times required to obtain relief from a headache for patients taking one of the meds. From a RS of 75 people with chronic headaches, 38 were randomly assigned to med R and the remaining 37 were assigned to med S. The time, in minutes, until each person experienced relief from a headache was recorded. The x̄ times were calculated for each med. Have the conditions been met for inference with a confidence interval for the diff. in μ? A: Yes, all conditions have been met B: No, because the data were not collected using a random sample C: No, because cause and effect cannot be inferred since there is a random sample D: No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is approximately normal E: No, because the sample sizes are not the sa

A: Yes, all conditions have been met The medications were randomly assigned to treatments, so the independence condition is met. Each sample size is greater than 30, so the condition that the distribution of sample means is approximately normal has also been met

Random samples of players for two types of video games were selected, and the mean number of hours per week spent playing the games was calculated for each group. The sample means were used to construct the 90% CI (1.5, 3.8) for the difference in the mean number of hours per week spent playing the games. The maker of one of the video games claims that there is a difference in the population mean number of hours per week spent playing the two games. Is the claim supported by the interval? A: Yes, because 0 is not contained in the interval B: Yes, because the midpoint of the interval is greater than 1 C: Yes, because the margin of error for the estimate is less than 1 D: No, because the margin of error for the estimate is greater than 1 E: No, because 0 is not contained in the interval

A: Yes, because 0 is not contained in the interval If there were no difference in the population means, the difference would be 0. Because 0 is not contained in the interval, 0 is not a plausible value for the population difference in means. There is evidence supporting the claim that there is a difference in the population mean number of hours per week spent playing the two games

A national travel association with over 3,000 members selected a random sample of 100 members of the association. The selected members were asked to report the number of miles they traveled on their last vacation. The mean and standard deviation of the responses were 150 miles and 40 miles, respectively. A graph of the sample data displayed a right skew. The association will construct a confidence interval to estimate the mean number of miles traveled for all members. Have the conditions for inference been met? A: Yes. All conditions for inference have been met B: No. The distribution of sample data was not approximately normal C: No. The sample size was greater than 10% of the population size D: No. The sample was not selected at random E: No. The sample consisted only of members of the travel association

A: Yes. All conditions for inference have been met All conditions have been met. The sample was selected at random, the sample size was less than 10% of the population size, and although the sample data had right skew, based on the central limit theorem, the sample size was large enough to assume normality of the sample means (100 > 30)

A team of ecologists will select a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. Which of the following is a correct inference procedure for the ecologists to use? A: A one-sample t-interval for a sample mean B: A one-sample t-interval for a population mean C: A one-sample t-interval for a population proportion D: A two-sample t-interval for a difference between means E: A two-sample t-interval for a difference between proportions

B: A one-sample t-interval for a population mean The researchers are interested in estimated the average number of eggs per nest, not a proportion. The correct procedure to estimate the average number in the population is the one-sample t-interval

Researchers for a company that manufactures batteries want to test the hypothesis that the mean battery life of their new battery is greater than the known mean battery life of their older version. The researchers selected random samples of 32 of the new batteries, subjected the batteries to continuous use, and determined the mean and standard deviation of the battery lives in the sample. Which of the following is an appropriate test for the researchers' hypothesis? A: A one-sample z-test for a population mean B: A one-sample t-test for a population mean C: A one-sample z-test for a population proportion D: A matched-pairs t-test for a mean difference E: A two-sample t-test for a difference between means

B: A one-sample t-test for a population mean The t-test is appropriate, because the population standard deviation for the new-version batteries is unknown, and the sample standard deviation will be used

The weekly sales at two movie theaters were recorded for a random sample of 25 weeks. A 95 percent confidence interval for the difference in mean weekly sales for the two movie theaters was calculated as ($1,288, $2,586). With all else remaining constant, which of the following would have resulted in a confidence interval narrower than the calculated interval? A: A sample size less than 25 B: A sample size greater than 25 C: An increase to 99 percent confidence D: A sample mean greater than $1,937 E: A sample mean less than $1,937

B: A sample size greater than 25 An increase in sample size will create a narrower interval

A researcher in sports equipment is investigating the design of racing swimsuits for women. The researcher selected a sample of 40 women swimmers from high school swim teams in the state and randomly assigned each swimmer to one of two groups: suit A or suit B. The women will wear the assigned suits for a certain race, and the mean swim times for each group will be recorded. The difference in the sample mean swim times will be calculated. Which of the following is the appropriate inference procedure for analyzing the results? A: A two-sample t-interval for a difference between sample means B: A two-sample t-interval for a difference between population means C: A one-sample t-interval for a sample mean D: A one-sample t-interval for a population mean E: A matched pairs t-interval for a mean difference

B: A two-sample t-interval for a difference between population means There were two independent groups in the experiment and data were collected on a single quantitative variable (swim times). The correct procedure is the two-sample t-interval for a difference in population means

A study will be conducted to investigate whether there is a difference in pain relief for two brands of headache pills, N and P. Participants will be randomly assigned to one of two groups. One group will take pill N when they experience a headache, and the other group will take pill P when they experience a headache. Each participant will record the number of minutes it takes until relief from the headache is felt. The mean number of minutes will be calculated for each group. Which of the following is the appropriate test for the study? A: A two-sample z-test for a difference between population proportions B: A two-sample t-test for a difference between population means C: A matched pairs t-test for a mean difference D: A one-sample z-test for a population proportion E: A one-sample t-test for a population mean

B: A two-sample t-test for a difference between population means Two random samples will be selected on a quantitative variable, and the difference in the sample means will be calculated. The appropriate test is the two-sample t-test for a difference in means

Researchers on car safety studied driver reaction time and cell phone use while driving. Participants in the study talked on either a hands-free phone or a handheld phone while driving in a car simulator. A two-sample t-test or a diff. in means was conducted to investigate whether the mean driver reaction time between the two groups of participants was different. All conditions for inference were met, and the test produced a test statistic of t = -2.763 and a p-value of 0.03. Which of the following is a correct interpretation of the p-value? A: AttMRTfHFaHP are =, the prob. of obtaining a TS < -2.763 is 0.03 B: AttMRTfHFaHP are =, the probability of obtaining a TS > 2.763 or < -2.763 is 0.03 C: AttMRTfHFaHP are ≠, the prob. of obtaining a TS < -2.763 is 0.03 D: AttMRTfHFaHP are ≠, the prob. of obtaining a TS > 2.763 or < -2.763 is 0.03 E: The prob. that the MRTfHFP will be < that for handheld phones is 0.03

B: Assuming that the mean reaction times for hands-free and handheld phones are equal, the probability of obtaining a test statistic greater than 2.763 or less than -2.763 is 0.03 The test is two-sided. The p-value is the combined area under the t-curve to the left of -2.763 and to the right 2.763. The combined area of 0.03 represents the probability of obtaining a test statistic of at most -2.763 or at least 2.763 if the null hypothesis of no difference in mean reaction time is true

Hannah wanted to investigate whether there was a difference in the time spent in the checkout line between two grocery stores in a large city. She went to grocery store J on a Monday morning and recorded the time, in minutes, it took 30 customers to go through a checkout line. Then she went to grocery store K on Monday afternoon and recorded the time it took 30 customers to go through a checkout line. Hannah calculated the mean number of minutes for the customers in each line. She intends to conduct a two-sample t-test for a difference in means between the two stores. Have all conditions for inference been met? A: Yes, all conditions have been met B: No, the data were not collected using a random method C: No, the sample sizes are greater than 10% of the population D: No, the sample sizes are not large enough to assume normality of the samp. distr. E: No, the distr. of the sample data are not approx. normal

B: No, the data were not collected using a random method There is no indication that the data were collected in a random manner. Hannah could have randomly selected the days, the times, and the checkout lines for collecting data from each store

A random sample of size 32 is selected from population X, and a random sample of size 43 is selected from population Y. A 90 percent confidence interval to estimate the difference in means is given as (-1.25, 0.87). Consider a change in the sample sizes such that a random sample of size 52 is selected from population X and a random sample of size 63 is selected from population Y. When all other things remain the same, what effect would such a change have on the interval? A: The width of the interval will increase B: The width of the interval will decrease C: The interval will contain no negative numbers D: The level of confidence will increase E: The sample means will increase

B: The width of the interval will decrease Go to image for explanation

A two-sample t-test for a difference in means was conducted to investigate whether the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. With all conditions for inference met, the test produced a test statistic of t = -2.073 and a p-value of 0.042. Based on the p-value and a significance level of α = 0.05, which of the following is a correct conclusion? A: There is CSE that the ATtSaLwtFS is less than the ATtSaLwtBS B: There is CSE that the ATtSaLwtFS is different from the ATtSaLwtBS C: There is not CSE that the ATtSaLwtFS is greater than the ATtSaLwtBS D: There is not CSE that the ATtSaLwtFS is different from the ATtSaLwtBS E: There is not CSE that the ATtSaLwtFS is less than the ATtSaLwtBS

B: There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke Since the p-value is less than the value of α (0.042 < 0.05), the null hypothesis would be rejected. There is convincing statistical evidence to conclude the alternative hypothesis is correct; that is, the average swim times are different for a lap with the freestyle stroke and a lap with the butterfly stroke

Engineers at a tire manufacturing company investigated the effect of a new rubber compound on the tire life of a certain brand of tires. From a sample of 16 tires, the engineers constructed a 99% CI for the mean tire life, in miles, as 62,550 ± 2,026. Suppose the company intends to claim a maximum tire life for advertising purposes. Based on the interval, of the following, which is the maximum plausible value for the mean tire life, in miles? A: 64,000 B: 64,250 C: 64,500 D: 64,750 E: 65,000

C: 64,500 The confidence interval is (60,524, 64,576). Of the listed tire life values, the maximum value that is contained in the interval is 64,500

To study learned behavior in mice, researchers used a sample of mice in a maze experiment. Each mouse had to find its way through a maze to reach food at the end. The mouse was timed on its first run through the maze and again on its tenth run through the maze. The difference in the times was recorded for each mouse. Which of the following is the most appropriate inference procedure for the researchers to use? A: A two-sample z-interval for a difference between proportions B: A two-sample t-interval for a difference between means C: A matched-pairs t-interval for a mean difference D: A one-sample z-interval for a population proportion E: A one-sample t-interval for a sample mean difference

C: A matched-pairs t-interval for a mean difference Two observations were recorded for each mouse, the first-run time and the tenth-run time. Since observations are paired for each mouse, the best method is a matched-pairs t-interval

To test the durability of phone screens, phones are dropped from a height of 1m until they break. A RS of 40 phones was selected from each of 2 manufacturers. The phones in the samples were dropped until the screens broke. The diff. in the mean # of drops was recorded and used to construct the 90% CI (0.46, 1.82) to estimate the pop. diff. in means. Consider the samp. procedure taking place repeatedly. Each time samples are selected, the phones are dropped and the stats are used to construct a 90% CI for the diff. in means. Which of the following statements is a correct interpretation of the int.? A: Approx. 90% of the int. will extend from 0.46 to 1.82 B: Approx. 90% of the int. constructed will capture the diff. in x̄ C: Approx. 90% of the int. constructed will capture the diff. in μ D: Approx. 90% of the int. constructed will capture ≥1 of the x̄ E: Approx. 90% of the int. constructed will capture ≥1 o

C: Approximately 90 percent of the intervals constructed will capture the difference in population means The level of 90 percent refers to the number of intervals that will capture the population difference in means if the process is repeated over and over again with samples of the same size

A two-sample t-test for a difference in means was conducted to investigate whether defensive players on a football team can bench-press more weight, on average, than offensive players. The conditions for inference were met, and the test produced a test statistic of t = 1.083 and a p-value of 0.15. Based on the p-value and a significance level of α = 0.05, which of the following is the correct conclusion? A: Reject Ho because 0.15>0.05. There is not CE that DPCBPMWoATOP B: Reject Ho because 0.15>0.05. There is CE that DPCBPMWoATOP C: Fail to reject Ho because 0.15>0.05. There is not CE DPCBPMWoATOP D: Fail to reject Ho because 0.15>0.05. There is CE DPCBPMWoATOP E: Fail to reject Ho because 0.15>0.05. There is CE that defensive players can bench press the same amount of weight, on average, as offensive players

C: Fail to reject the null hypothesis because 0.15>0.05. There is not convincing evidence that defensive players can bench-press more weight, on average, than offensive players Because p > α, the null hypothesis should not be rejected, indicating there is not convincing evidence to support the alternative hypothesis

A biologist studied the freq. of croaks for frogs from 2 diff. regions. From a RS of 32 frogs located in the northern region, the mean number of croaks per hour was 21.3, and from a RS of 38 frogs located in the southern region, the mean number of croaks per hour was 28.9. To estimate the diff. in the mean number of croaks (southern - northern), a 95% CI was constructed from the samples. The int. was reported as (7.1, 8.1). Which of the following claims is supported by the int.? A: All southern frogs croak more times per hour than do all northern frogs B: The northern frogs are likely to have a greater mean number of croaks per hour than the southern frogs C: The southern frogs are likely to have a greater mean number of croaks per four than the northern frogs D: All frogs in the study have about the same number of croaks per hour E: The northern and southern frogs have the same mean number of croaks per hour

C: The southern frogs are likely to have a greater mean number of croaks per four than the northern frogs All values in the interval are positive, and the interval was built from the difference in sample means, 29.8 - 21.3. It is likely the southern population mean is greater than the northern population mean

To prepare for a certification exam, candidates can use one of two exam preparation books, book J or book K. A two-sample t-test for a difference in means was conducted to investigate whether the average score on the exam for candidates using book J is less than the average score for candidates using book K. With all conditions for inference met, the test produced a test statistic of t = -1.356 and a p-value of 0.101. Based on the p-value and a significance level of α = 0.05, which of the following is a correct conclusion? A: There is CSE that the ASoCUBJ is equal to the ASoCUBK B: There is CSE that the ASoCUBJ is less than the ASoCUBK C: There is not CSE that the ASoCUBJ is less than the ASoCUBK D: There is not CSE that the ASoCUBJ is different from the ASoCUBK E: There is not CSE that the ASoCUBJ is greater than the ASoCUBK

C: There is not convincing statistical evidence that the average score of candidates using book J is less than the average score of candidates using book K Because p > α, the null hypothesis is not rejected. There is not convincing evidence to support the alternative hypothesis

An environmentalist agency frequently samples the water in a region to ensure that the levels of a certain contaminant do not exceed 30 parts per billion (ppb). From 12 randomly selected samples of the water, the agency constructed the 99% CI (22.5, 28.7). Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval? A: For all water in the region, 99% of the water contains a level of the contaminant between 22.5 and 28.7 B: We are 99% confident that the mean level of the contaminant in the sample is between 22.5 and 28.7 C: We are 99% confident that the mean level of the contaminant in all the water in the region is between 22.5 and 28.7 D: There is a 0.99 prob. that the mean level of the contaminant in the sample is between 22.5 and 28.7 E: There is a 0.99 prob. that the mean level of the contaminant in all the water in the region is between 22.5 and 28.7

C: We are 99% confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb The percent is how much confidence exists that the interval has captured the population mean

Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected and analyzed a random sample of 40 different types of Brand A shoes and 33 different types of brand B shoes. Alicia observes that the boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means. Is the sampling distribution of the difference in sample means approximately normal? A: Yes, because Alicia selected a random sample B: Yes, because for each brand it is reasonable to assume that the population size is greater than ten times its sample size C: Yes, because the size of each sample is at least 30 D: No, because the distribution of Brand A shoes has outliers E: No, because the shape of the population distribution is unknown

C: Yes, because the size of each sample is at least 30 Although the boxplot shows outliers, both sample sizes (40 and 33) are greater than 30, so based on the central limit theorem, the distribution of the difference in sample means is approximately normal

The local ranger station tracked and tagged 2,844 adult female black bears in a national park. A random sample of 9 adult female black bears from those tagged had an average body weight of 203 pounds with standard deviation 25 pounds. Which of the following is a point estimate for the population mean weight of all female black bears that are tagged? A: 9 B: 25/sqrt(9) C: 25 D: 203 E: 2,844

D: 203 The mean weight of the sample acts as a point estimate for the mean weight of the population

A researcher's hypothesis is that the average length of salmon returning to spawn from an Alaskan river is less than the historical average length of 24 inches. The researcher collects a random sample of 45 salmon, measures the length of each fish, and computes an average length of 22 inches, with a standard deviation of 3.1 inches. Which of the following is the appropriate test for the researcher's hypothesis? A: A matched-pairs t-test for a mean difference B: A two-sample t-test for a difference between means C: A one-sample z-test for a population mean D: A one-sample t-test for a population mean E: A one-sample z-test for a population proportion

D: A one-sample t-test for a population mean The sample standard deviation will be used, so the t-test is the appropriate test

The distribution of mass for United States pennies minted since 1982 is approximately normal with mean 2.5 grams. A random sample of 10 pennies minted since 1982 was selected. The sample had a mean mass of 2.47 grams and a standard deviation of 0.04 gram. The test statistic for the population mean has which of the following distributions? A: A normal distribution with mean 0 and standard deviation 1 B: A normal distribution with mean 2.5 and standard deviation 0.04 C: A normal distribution with mean 2.47 and standard deviation 0.04 D: A t-distribution with 9 degrees of freedom E: A t-distribution with 10 degrees of freedom

D: A t-distribution with 9 degrees of freedom When the sample standard deviation is used instead of the population standard deviation, the test statistic follows a t-distribution with degrees of freedom equal to the sample size minus 1. In this case, the sample size was 10, so there are 9 degrees of freedom

A snowboarding competition site is using a new design for the parallel giant slalom. The designer of the slalom is investigating whether there is a difference in the mean times taken to complete a run for men and women competitors. As part of the investigation, independent random samples of men and women who will use the slalom run are selected and their times to complete a run are recorded. Which of the following is the appropriate inference procedure by which the designer can estimate the difference in the mean completion times for men and women? A: A one-sample t-interval for a sample mean B: A one-sample t-interval for a population mean C: A matched pairs t-interval for a mean difference D: A two-sample t-interval for a difference between population means E: A two-sample t-interval for a difference between sample means

D: A two-sample t-interval for a difference between population means With two independent random samples from the two populations (men and women snowboarders), the correct procedure is the two-sample t-interval for a difference in population means

A study was conducted to investigate whether the mean price of a dozen eggs was different for two different grocery stores, Store A and Store B, in a large city. A carton of one dozen eggs from each store was randomly selected for each of 35 weeks, for a total sample size of 35 cartons from each store. The mean price of the 35 cartons was recorded for each store. The difference in the mean carton price for the stores will be calculated. Which of the following is the appropriate test for the study? A: A one-sample z-test for a population proportion B: A one-sample t-test for a sample mean C: A matched pairs t-test for a mean difference D: A two-sample t-test for a difference between population means E: A two-sample z-test for a difference between population proportions

D: A two-sample t-test for a difference between population means Two random samples are selected on a quantitative variable, and the difference in the sample means will be calculated. The appropriate test is the two-sample t-test for a difference in population means

Zoologists studying two populations of tigers conducted a two-sample t-test for the difference in means to investigate whether the tigers in population X weigh more, on average, than the tigers in population Y. Two independent random samples were taken, and the difference between the sample means was calculated. All conditions for inference were met, and the test produced a p-value of 0.02. Which of the following is a correct interpretation of the p-value? A: The prob. that the MWfTiPX is greater than that for PY is 0.02 B: The prob. that the MWfTiPX is equal to that for PY is 0.02 C: AttMWfPXaY are equal, the prob. of observing a diff. equal to the sample diff. is 0.02 D: AttMWfPXaY are equal, the prob. of observing a diff. as great or greater than the sample diff. is 0.02 E: AttMWfPX is greater than the MWfPY, the prob. of observing a diff. as great as or greater than the sample diff. is 0.02

D: Assuming that the mean weights for population X and Y are equal, the probability of observing a difference as great or greater than the sample difference is 0.02 The test is right-tailed because in the investigation, the zoologists believe that one population weighs more than the other. The p-value is the area under the t-curve to the right of the test statistic created from the sample difference. In this case, the area of 0.02 is the probability of observing a difference equal to or greater than the sample difference if there is no difference in the mean tiger weights of the two populations

An experiment was conducted to determine whether the price of a golf club affected the distance a golfer could hit a golf ball. A sample of 60 golfers were RA to 1 of 2 groups, C or E. The 30 golfers in group C were given a club and told the price of was cheap; the 30 golfers in group E were given the same club and told the price was expensive. In reality, there was no diff. in price. The golfers used their assigned clubs to hit a golf ball as far as they could. The distance, in yards, that each golfer hit the ball was recorded, and the mean distance calculated for each group. A two-sample t-test for a diff. in means will be conducted. Which of the following statements are true? I. The data were collected using RA II. The data were collected using RS III. The dist. of the diff. in x̄ will be approx. normal A. I only B: II only C: III only D: I and III only E: I, II, and III

D: I and III only The data were collected using random assignment since the 60 golfers were randomly assigned to treatment groups, so statement I is true. It was not indicated that the 60 golfers in the sample were randomly selected, so statement II is not true. The distribution will be approximately normal since each group size is large enough, so statement III is true

A magazine article reported that college students spend an average of $100 on a first date. A university sociologist believed that number was too high for the students at the university. The sociologist surveyed 32 RS students from the university and obtained a x̄ of $92.23 for the most recent first dates. A one-sample t-test resulted in a p-value of 0.026. Which of the following is a correct interpretation of the p-value? A: The prob. is 0.026 that the MAoMSftUSoaFD is <$100 B: The prob. is 0.026 that the MAoMSftUSoaFD is <$92.23 C: The prob. is 0.026 that the MAoMSftUSoaFD is >$92.23 D: If the MAoMtSftUSotFD is $100, the prob. is 0.026 that a RS group of 32 SftU would spend a mean of $92.23 or less on their most recent first dates E: If the MAoMtSftUSotFD is <$100, the prob. is 0.026 that a RS group of 32 SftU would spend a mean of $92.23 or less on their most recent first dates

D: If the mean amount of money that students from the university spend on the first date is $100, the probability is 0.026 that a randomly selected group of 32 students from the university would spend a mean of $92.23 or less on their most recent first dates The p-value is the probability that, if many samples of size 32 were selected from the students of the university, we would observe a sample mean of $92.23 or less, given that the population mean is $100

Health programs routinely study the number of days that patients stay in hospitals. In one study, a random sample of 12 men had a mean of 7.95 days and a standard deviation of 6.2 days, and a random sample of 19 women had a mean of 7.1 days and a standard deviation of 5.0 days. The sample data will be used to construct a 95 percent confidence interval to estimate the difference between men and women in the mean number of days for the length of stay at a hospital. Have the conditions been met for inference with a confidence interval? A: Yes. All conditions have been met B: No. The data were not collected using a random method C: No. The size of at least one of the samples is greater than 10 percent of the population D: No. The sample sizes are not large enough to assume that the sampling distribution of the difference in sample means is approximately normal E: No. The sample sizes are not the same

D: No. The sample sizes are not large enough to assume that the sampling distribution of the difference in sample means is approximately normal Each sample size is less than 30, and information about the distributions of the populations is not known. Therefore, normality cannot be assumed for the sampling distribution of the difference in sample means

Which of the following correctly compares the t-distribution and z-distribution? A: For small sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric B: For large sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric C: The curves of both distributions are symmetric, but the height of the density curve of the t-distribution is taller than the height of the density curve of the z-distribution D: The area under the density curve of the t-distribution is greater than the area under the density curve of the z-distribution, especially for small sample sizes E: The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes

E: The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes The t-curve tends to be lower and wider than the z-curve, especially when the sample size is small

For a certain brand of tomato seeds, the seed package claims that it takes 87 days after planting for the tomato plants to produce fruit. Sarah, a botanist, wanted to know whether the mean number of days for the plants to produce fruit where she lives is difference from 87 days. She planted 40 seeds and recorded the number of days for each plant to produce fruit. With all conditions for inference met, the hypothesis test was conducted at the significance level α = 0.05, and the test resulted in a p-value of 0.0752. Which of the following is a correct conclusion? A: Sarah has CSEtC that the PMNoDftPtPF is >87 days B: Sarah has CSEtC that the PMNoDftPtPF is different from 87 days C: Sarah does not have CSEtC that the PMNoDftPtPF is >87 days D: Sarah does not have CSEtC that the PMNoDftPtPF is different from 87 days E: Sarah does not have CSEtC that the PMNoDftPtPF is equal to 87 days

D: Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days The p-value of 0.0752 is greater than the significance level of 0.05, and the null hypothesis is not rejected. There is not convincing statistical evidence to support the alternative hypothesis that the mean time is different from 87 times

Researchers at a medical center studied the amount of caffeine, in milligrams (mg), contained in a 16oz cup of coffee made at one machine at the center's cafeteria. They selected a RS of 40 16-oz cups of coffee made at different times of the day during one month. The mean and standard deviation of the amount of caff. in the sample were 159.88 mg and 36.72 mg, respectively. A graph of the sample data revealed a right skew with one outlier. The researchers will construct a CI to estimate the amount of caff. for all 16oz cups made at the machine. Which of the following conditions is not needed for the inference? A: The samples were selected at random B: The observations are independent of one another C: The sample of size 40 is < 10% of the population size D: The graph of the sample data is symmetric with no outliers E: The sample size is large enough to assume that the samp. dist. of sample means is approx. normal

D: The graph of the sample data is symmetric with no outliers Because the sample size is large enough (40 > 30), the assumption of normality of sample means holds, regardless of the shape of the distribution of the sample data

Most dermatologists recommend that the ideal shower lasts approx. 10 min. A researcher suspects that the average shower length of high school students is greater than 10 min. To test the belief, the researcher surveyed 125 randomly selected high school students and found that their average shower length was 14.7 min. With all conditions for inference met, a HT was conducted at the significance level of α = 0.05, and the test produced a p-value of 0.000. Which of the following is the appropriate conclusion? A: The test was flawed because the p-value cannot equal 0 B: The researcher has SE to conclude that the sample mean SLfHSS is >10 min C: The researcher does not have SE to conclude that the sample mean SLfHSS is >10 min D: The researcher has SE to conclude that the population mean SLfHSS is >10 min E: The researcher does not have SE to conclude that the population mean SLfHSS is >10 min

D: The researcher has statistical evidence to conclude that the population mean shower length for high school students is greater than 10 minutes The p-value of 0.0000 is less than the significance level of 0.05, and the correct decision is to reject the null hypothesis. There is statistical evidence to support the alternative hypothesis and conclude that the population mean shower length for high school students is greater than 10 minutes

To assess the effectiveness of a kindergarten-readiness program, 15 children from a RS were each given a diagnostic assessment before beginning the program and a follow-up assessment after completing the program. For each child, the diff. in the score points between the two assessments was calculated and used to create the 95% CI (20.1, 23.9). Assuming all conditions are met, which of the following is a correct interpretation of the interval? A: For all CitP, 95% of the children will have a mean diff. in scores of between 20.1 and 23.9 B: There is a 0.95 prob. that the mean diff. in scores for all CitS is between 20.1 and 23.9 C: There is a 0.95 prob. that the mean diff. in scores for the CitP is between 20.1 and 23.9 D: We are 95% confident that the mean diff. in scores for all CitP is between 20.1 and 23.9 E: We are 95% confident that the mean diff. in scores of the CitS is between 20.1 and 23.9

D: We are 95% confident that the mean difference in scores for all children in the program is between 20.1 points and 23.9 points The percent is how much confidence exists that the interval has captured the population mean

A sports equipment researcher investigated how different types of wood used to make baseball bats might affect betting. The researcher selected a sample of 80 batters from summer baseball leagues and randomly assigned the batters to one of two groups: the ash bat group or the maple bat group. The mean number of hits for each group was recorded at the end of the season, and the difference in the sample means was calculated. Which of the following is the appropriate inference procedure for analyzing the results of the investigation? A: A one-sample t-interval for a population mean B: A one-sample t-interval for a sample mean C: A matched pairs t-interval for a mean difference D: A two-sample t-interval for a difference between sample means E: A two-sample t-interval for a difference between population means

E: A two-sample t-interval for a difference between population means There were two independent groups in the experiment and data was collected on a single quantitative variable (number of hits). The correct procedure is the two-sample t-interval for a difference in population means

Animal scientists studied foraging behavior of the scrub lizard, found in central Florida. Foraging is the process of searching for food. To study such behavior, the scientists recorded the number of head movements per minute for a sample of 63 lizards. A 95% CI constructed from the sample is given as 2.7 ± 0.62 head movements per minute. Based on the interval, is a claim of 3 head movements per minute plausible? A: The claim is not plausible because 3 head movements per minute is contained within the interval B: The claim is not plausible because 3 head movements per minute is not contained within the interval C: The claim is not plausible because 95% of 3 is greater than the sample mean of 2.7 D: The claim is plausible because 3 head movements per minute is not contained within the interval E: The claim is plausible because 3 head movements per minute is contained within the interval

E: The claim is plausible because 3 head movements per minute is contained within the interval The claim is plausible. The interval gives plausible values of the population mean, and the confidence interval extends from 2.08 to 3.32. Because the value 3 is contained in the interval, it is a plausible value for the population mean

Animal researchers studying cows and horses conducted a two-sample t-test for a diff. in means to investigate whether grazing cows eat more grass, on average, than grazing horses. All conditions for inference were met, and the test produced a test statistic of t = 1.664 and p-value of 0.0487. Which of the following is a correct interpretation of the p-value? A: The prob. that cows eat more grass than horses, on average, is 0.0487 B: The prob. that cows eat the same amount of grass as horses, on average, is 0.0487 C: Assuming that the MAoGEbC is greater than the mean amount of grass eaten by horses, the probability of observing a test statistic of at most 1.664 is 0.0487 D: Assuming that the MAoGEbC is equal to the MAoGEbH, the prob. of observing a test statistic of at most 1.664 is 0.0487 E: Assuming that the MAoGEbC is equal to the MAoGEbH, the prob. of observing a test statistic of at least 1.664 is 0.0487

E: Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at least 1.664 is 0.0487 The test is right-tailed, since the investigator is looking at whether cows eat more grass than horses. The p-value is the are under the t-curve to the right of t = 1.664. The area of 0.0487 represents the probability of obtaining a test statistic equal to or greater than 1.644 if the null hypothesis is true; that is, if the mean amounts eaten by cows and horses are equal

A soda manufacturer claims that its Cherry Fizz soda has more carbonation than a competitor's Cherry Eclipse soda. Bottles of both types of soda are opened, covered with a balloon, and then shaken. The diameter of each balloon is then measured. The mean balloon diameters are 2.3 in. for the Cherry Fizz soda and 2.1 in. for the Cherry Eclipse soda. A 90% CI to estimate the diff. in mean diameters, in inches, is (-0.8, 1.2). Which of the following claims is supported by the int.? A: B/c 2.3 in. is larger than 2.1 in., the manufacturer is correct, and Cherry Fizz has more carbonation B: B/c the int. has more pos values than neg values, Cherry Fizz has more carbonation C: B/c 2.3 and 2.1 are very similar, there is no diff. in the mean carbonation levels D: The int. can't be interpreted b/c neg measurements are not possible E: B/c the int. contains 0, it is possible that there is no diff. in mean carbonation levels

E: Because the interval contains 0, it is possible that there is no difference in mean carbonation levels Intervals that contain 0 indicate that it is plausible that there is no difference between the population means. There is not have convincing evidence that Cherry Fizz has more carbonation than Cherry Eclipse

A manufacturer of piston rings for automobile engines frequently tests the width of the rings for quality control. Last week, a random sample of 15 rings were measured, and the mean and standard deviation of the sample were used to construct a 95% CI for the population mean width of the rings. When all other things remain the same, which of the following conditions would have resulted in a wider interval than the one constructed? I. A sample size of 20 with 95% confidence II. A sample size of 15 with 99% confidence III. A sample size of 12 with 95% confidence A: I only B: II only C: III only D: I and II E: II and III

E: II and III Both statements II and III give conditions that increases the width of the interval. With all else remaining the same, the width of a confidence interval increases if sample size decreases or if confidence level increases

A bank manager wants the average time that a customer waits in line to be at most 3 min. Customers at the bank have complained about the long wait times. To test whether the average wait time at the bank is >3 min, 60 customers were randomly selected as they entered the bank and their wait times were recorded. The mean wait time was 4.7 min. A one-sample t-test resulted in a p-value of 0.00031. Which of the following is an appropriate interpretation of the p-value? A: The prob. that the population mean wait time is >3 min is 0.00031 B: The prob. that the sample mean wait time is >3 min is 0.00031 C: If the μ wait time is >3 min, the prob. of observing a sample mean wait of 4.7 or more min is 0.00031 D: If the μ wait time is 3 min, the prob. of observing a sample mean wait time of 4.7 min is 0.00031 E: If the μ wait time is 3 min, the prob. of observing a sample mean wait time of 4.7 min or more is 0.00031

E: If the population mean wait time is 3 minutes, the probability of observing a sample mean wait time of 4.7 minutes or more is 0.00031 If the null hypothesis is true and the mean is 3 minutes, the p-value is the probability of observing the sample mean of 4.7 minutes or more

A 99 percent confidence interval for a difference in means was given as 25.1±4.3. Assuming all conditions for inference were met, which of the following is a correct interpretation of the 99 percent confidence level? A: In repeated samples of the same size, approximately 99 percent of the intervals constructed from the samples will extend from 20.8 to 29.4 B: In repeated samples of the same size, approximately 99 percent of the sample means will fall between 20.8 and 29.4 C: In repeated samples of the same size, approximately 99 percent of the samples will fall between 20.8 and 29.4 D: In repeated samples of the same size, approximately 99 percent of the intervals constructed from the samples will capture the difference in sample means E: In repeated samples of the same size, approximately 99 percent of the intervals constructed from the samples will capture the difference in population means

E: In repeated samples of the same size, approximately 99 percent of the intervals constructed from the samples will capture the difference in population means The level of 99% refers to the number of intervals that will capture the difference in population means if the process is repeated over and over again with samples of the same size

The director of fitness for a large corporation with over 5,000 employees recorded the resting heart rate, in beats per minute (bpm), for 35 employees who were known to wear activity trackers. The following boxplot summarizes the result. The director wants to estimate the resting heart rate for all employees with a confidence interval. Have all conditions for inference been met? A: Yes, all conditions have been met B: No, the distribution of the sample data is not approximately symmetric C: No, the sample size is greater than 10 percent of the population size D: No, the distribution of resting heart rate in the population cannot be assumed to be approximately normal E: No, the sample was not selected at random

E: No, the sample was not selected at random Only employees wearing activity trackers were used in the sample. It is not reasonable to believe that these employees are representative of all 5,000 employees, because there will be some employees who do not wear activity trackers

Porcupines can cause damage to wood structures by chewing them. Researchers studied a liquid repellent designed to reduce such damage. A sample of 20 wooden blocks of the same size were treated with the repellent and left outside in an area where porcupines are known to live. After a certain amount of time, the blocks were inspected for the number of porcupine teeth marks (PTM) visible. The data were used to create the 95% CI (4.9, 5.8). Which of the following claims is supported by the interval? A: The expected number of PTM on a wooden block treated with the repellent is less than 5 B: The expected number of PTM on a wooden block treated with the repellent is 5 C: The mean number of PTM on all wooden blocks treated with the repellent is 6 D: The mean number of PTM on all wooden blocks treated with the repellent is > than 6 E: The mean number of PTM on all wooden blocks treated with the repellent is < than 6

E: The mean number of porcupine teeth marks on all wooden blocks treated with the repellent is less than 6 All plausible values for the population mean, 4.9 to 5.8, are less than 6

A car company claims that its new car, the GoFast2000, has a gas mileage of 35 mpg. A consumer group suspects that the true mean gas mileage of the new cars is less than 35 mpg. The group test 50 randomly selected GoFast2000 cars and finds a sample mean of 34.8 mpg. With all assumptions for inference met, a hypothesis test resulted in a p-value of 0.324. For a significance level of α = 0.05, which of the following is a correct conclusion? A: The p-value is <0.05, and Ho is rejected. There is CSE that the mean is less than 35 mpg B: The p-value is <0.05, and Ho is not rejected. There is not CSE that the mean is less than 35 mpg C: The p-value is >0.05, and Ho is rejected. There is not CSE that the mean is less than 35 mpg D: The p-value is >0.05, and Ho is not rejected. There is CSE that the mean is 35 mpg E: The p-value is >0.05, and Ho is not rejected. There is not CSE that the mean is less than 35 mpg

E: The p-value is greater than 0.05, and the null hypothesis is not rejected. There is not convincing statistical evidence that the mean is less than 35 mpg The null hypothesis is not rejected because the p-value of 0.324 is greater than the significance level of 0.05. There is not convincing statistical evidence to support the alternative hypothesis that the gas mileage is less than 35 mpg

A consumer group studied two different manufacturers of cars, J and K, to investigate differences in gas mileage for cars made by the two manufacturers. For a similar type of car, a RS of 15 cars from J and a RS of 12 cars from K were selected, and the gas mileages, in mpg, were recorded. The diff. in the sample mean gas mileages was used to construct the 90% CI (3.5, 5.7). Assuming all conditions for inference were met, which of the following is the correct interpretation of the interval? A: The prob. is 0.90 that the diff. in x̄ for GSftTCM is between 3.5 mpg and 5.7 mpg B: The prob. is 0.90 that the μ diff. in GSftTCM is between 3.5 mpg and 5.7 mpg C: About 90% of the diff. in GSftTCM are between 3.5 mpg and 5.7 mpg D: We are 90% conf. that the diff. in x̄ for GSftTCM is between 3.5 mpg and 5.7 mpg E: We are 90% conf. that the μ diff. of GSftTCM is between 3.5 mpg and 5.7 mpg

E: We are 90 percent confident that the population mean difference of gas mileage for the two car manufacturers is between 3.5 mpg and 5.7 mpg The 90 percent refers to the level of confidence that the interval has captured the population mean difference in gas mileage between the two car manufacturers

Two independent random samples were collected from the same population to estimate the population mean. Sample A had a sample size of 25 and a sample mean of 50. The 95% CI constructed from sample A had a margin of error of 4.2. Sample B had a sample size of n and a sample mean of x̄B. The k% CI constructed from sample B had a margin of error of 3.7. Assume both samples had the same sample standard deviation. Which of the following values from sample B explains why the margin of error for sample A is greater than the margin of error for sample B? Go to image for answers

For this response, the size of sample B is greater than the size of sample A and the confidence level of sample B is less than the confidence level of sample A. Both of these would result in a smaller margin of error for the confidence interval constructed from sample B

A software company provides specialized resort reservation software that can be tailored to the needs of its customers. The company's 120 customers pay yearly subscription costs that can vary from customer to customer. The company knows that to be profitable, it needs each customer to be spending at least $23,000 per year, on average. The company selects a random sample of 33 customers and computes a mean of $27,871 and a standard deviation of $309.10. It performs a hypothesis test and computes a very small p-value. The software company concludes that the mean is greater than $23,000. Was it appropriate for the software company to perform the hypothesis test and make the conclusion that was made? Go to image for answers

It is not appropriate to perform the hypothesis test. Because the sample size (33) is greater than 10 percent of the population size (120), it is not appropriate to proceed with the hypothesis test

A six-week fitness program was designed to decrease the time it takes retired individuals to walk one mile. At the beginning of the program, 20 randomly selected retired individuals were invited to participate, and their times to walk a mile were recorded. After the six-week program, their times to walk a mile were again recorded. Most participants saw little to no improvement in their times to walk one mile; however, a few participants saw drastic improvements in their times to walk one mile. The program director would like to perform a hypothesis test to determine if the program reduces the mean time for retired individuals to walk a mile. Which of the following statements is true? Go to image for answers

Since a few participants saw drastic improvement, the distribution of the sample data is skewed. Because the distribution is skewed and the sample size (20) is less than 30, the normality condition is not met

Last year the mean cost μ for a one-bedroom rental in a certain city was $1,200 per month. Eli is looking for a one-bedroom apartment and is investigating whether the mean cost is less now than what it was last year. A random sample of apartments had a sample mean x̄ of $1,180 per month. Assuming all conditions for inference are met, Eli will conduct a hypothesis test as part of his investigation. Which of the following is the correct set of hypotheses? Go to image for answers

The null hypothesis is a statement of the current population mean. The alternative hypothesis is a statement of Eli's investigation to see if the mean cost is less now.

The mean length μ pf male geckos is 9.5 inches. A researcher studying a population of geckos in a certain region will conduct a hypothesis test to investigate whether there is evidence that the mean length is greater than 9.5 inches. A random sample of geckos was selected, and the sample mean x̄ was calculated as 10 inches. Which of the following is the correct set of hypotheses? Go to image for answers

The null hypothesis is a statement of the current population mean. The alternative hypothesis is a statement of the researcher's investigation

To test the effectiveness of an exercise program in reducing high blood pressure, 15 participants had their blood pressures recorded before beginning the program and again after completing the program. The difference (after minus before) in blood pressure was recorded for each participant, and the sample mean difference x̄D was calculated. A hypothesis test will be conducted to investigate whether there is convincing statistical evidence for a reduction in blood pressure for all who complete the program. Which of the following is the correct set of hypotheses? Go to image for answers

The null hypothesis is a statement that there is no difference in population blood pressure before and after the program. The alternative hypothesis is a statement that blood pressure after the program is less than before, making the difference negative

Two siblings, Alice and Sean, are both convinced that they are faster than the other at solving a puzzle cube. They recorded the length of time it took them to solve the cube 18 times each during a one-month period. Then each calculated the mean amount of time and standard deviation, in minutes, for their times. Let μA equal the mean time it took Alice to solve the puzzle cube and μS equal the mean time it took Sean. Which of the following are the appropriate null and alternative hypotheses to test for a difference in time for the siblings to solve the cube? Go to image for answers

The null hypothesis states that the two population means are equal, and the alternative hypothesis states that they are not equal

A reporter responsible for the food section of a magazine investigated the belief that grocery stores sell beef at a higher price in the fall than in the spring. The reporter selected independent random samples of grocery-store beef prices in November and April and computed the mean and standard deviation for the samples. Which of the following are the correct null and alternative hypotheses for the reporter's investigation, where μF represents the mean price of beef in the fall and μS represent the mean price of beef in the spring? Go to image for answers

The null hypothesis states that there is no difference between the population mean price of beef in the fall and the population mean price of beef in the spring, and the alternative hypothesis states that the population mean price of beef is greater in the fall than in the spring

A company that packages salted and unsalted mixed nuts received a complaint that claimed that the company's salted packages contain more whole cashews than their unsalted packages do. The quality control department investigated the claim by randomly selecting a sample of 45 of each type of package, counting the number of cashews in each package, and finding the mean and standard deviation for both types of packages. Which of the following are the correct null and alternative hypotheses to test the complaint's claim, where μS is the mean number of cashews per package of salted nuts and μU is the mean number of cashews per package of unsalted nuts? Go to image for answers

The null hypothesis states that there is no difference in the mean number of whole cashews in the two types of packages, and the alternative hypothesis states that the mean number of cashews in the salted packages is greater than the mean number for the unsalted packages

For a certain brand of canned corn, the company claims that the mean weight of the contents of the cans is 15.25 ounces. A random sample of 36 cans were selected. The sample was found to have mean 15.18 ounces and standard deviation 0.12 ounce. A hypothesis test will be conducted to investigate whether there is evidence to support the belief that the mean is less than 15.25 ounces. Which of the following is the correct test statistic for the hypothesis test? Go to image for answers

The numerator of the test statistic is the sample mean (15.18) minus the assumed population mean (15.25). The denominator of the test statistic is the sample standard deviation (0.12) divided by the square root of the sample size (sqrt(36) = 6)

A century ago, the average height of adult women in the United States was 63 inches. Researchers believe that the average might be greater today. A random sample of 40 adult women was selected from the population. The sample had mean 64.2 inches and standard deviation 2.9 inches. Assuming all conditions for inference are met, the researchers will perform an appropriate hypothesis test to investigate their belief. Which of the following is the correct test statistic for the hypothesis test? Go to image for answers

The numerator of the test statistic is the sample mean (64.2) minus the hypothesized mean (63). The denominator of the test statistic is the sample standard deviation divided by the square root of the sample size (sqrt(40))

A random sample of 10 employees of a company was selected to estimate the mean one-way commute time for all employees at the company. The mean and standard deviation of the sample were 38 minutes and 6 minutes, respectively. Assuming all conditions for inference are met, which of the following is the margin of error, in minutes, for a 95 percent confidence interval for the population mean one-way commute time? Go to image for answers

The standard error is the sample standard deviation divided by the square root of the sample size, or 6/sqrt(10). With a sample size of 10, the number of degrees of freedom is equal to n-1 = 10-1 = 9, and the correct critical value is t* = 2.262