Unit 7 Progress Check: MCQ Part C
Researchers studying two populations of wolves conducted a two-sample t-test for the difference in means to investigate whether the mean weight of the wolves in one population was different from the mean weight of the wolves in the other population. All conditions for inference were met, and the test produced a test statistic of t=2.771 and a p-value of 0.01. Which of the following is a correct interpretation of the pp-value?
A. Assuming that the mean weights of wolves in the populations are equal, the probability of obtaining a test statistic that is greater than 2.771 or less than −2.771 is 0.01.
Two 95 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and J. One confidence interval, I400, will be constructed using samples of size 400 from each of R and J, and the other confidence interval, I100, will be constructed using samples size 100 from each of R and J. When all other things remain the same, which of the following describes the relationship between the two confidence intervals?
A. The width of I400 will be 4 times the width of I100.
Two ride-sharing companies, A and B, provide service for a certain city. A random sample of 52 trips made by Company A and a random sample of 52 trips made by Company B were selected, and the number of miles traveled for each trip was recorded. The difference between the sample means for the companies (A-B) was used to construct the 95 percent confidence interval (1.86, 2.15). Which of the following is a correct interpretation of the interval?
A. We are 95 percent confident that the difference in sample means for miles traveled by the two companies is between 1.86 miles and 2.15 miles.
A civil engineer tested concrete samples to investigate the difference in strength, in newtons per square millimeter (N/mm2)(N/mm2), between concrete hardened for 21 days and concrete hardened for 28 days. The engineer measured the strength from each sample, calculated the difference in the mean strength between the samples, and then constructed the 95 percent confidence interval, (2.9,3.1), for the difference in mean strengths. Assuming all conditions for inference were met, which of the following is a correct interpretation of the 95 percent confidence level?
B. In repeated samples of the same size, approximately 95 percent of the sample means will fall between 2.9 N/mm^2 to 3.1 N/mm^2.
A two-sample t-test for a difference in means was conducted to investigate whether there is a statistically significant difference in the average amount of fat found in low-fat yogurt and the average amount of fat found in nonfat yogurt. With all conditions for inference met, the test produced a test statistic of t=2.201t=2.201 and a pp-value of 0.027. Based on the pp-value and a significance level of α=0.05α=0.05, which of the following is the correct conclusion?
B. Reject the null hypothesis because p<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is statistically significant.
A consumer group selected 100 different airplanes at random from each of two large airlines. The mean seat width for the 100 airplanes was calculated for each airline, and the difference in the sample mean widths was calculated. the group used the sample results to construct a 95% confidence interval for the difference in population mean widths of seats between the two airlines. Suppose the consumer group used a sample size of 50 instead of 100 for each airline. When all other things remain the same, what effect would the decrease in sample size have on the interval?
B. The width of the confidence interval would increase.
A two-sample t-test for a difference in means was conducted to investigate whether the average wait time at a fast food restaurant in Town A was longer than the average wait time at a fast food restaurant in Town B. With all conditions for inference met, the test produced a test statistic of t=2.42 and a p-value of 0.011. Based on the pp-value and a significance level of α=0.02, which of the following is a correct conclusion?
B. There is convincing statistical evidence that the average wait time at the restaurant in Town A is longer than the average wait time at the restaurant in Town B.
A two-sample t-test will be conducted to investigate whether the mean number of tickets sold for children each day is less at movie theater J than at movie theater K. From a random sample of 50 days at theater J, the average was 75 children tickets with standard deviation 12. From a random sample of 60 days at theater K, the average was 85 children tickets with standard deviation 14. Under the assumption that there is no difference in the population means (J minus K), which of the following is the appropriate test statistic for the test?
B. t=75−85/√12^2/50+14^2/60
A study will be conducted to investigate whether there is a difference in the mean weights between two populations of raccoons. Random samples of raccoons will be selected from each population, and the mean sample weight will be calculated for each sample. Which of the following is the appropriate test for the study?
C. A two-sample t-test for a difference between sample means
A random sample of monarch butterflies and a random sample of swallowtail butterflies were selected, and the difference in the average flying speed for each sample was calculated. A two-sample t-test for the difference in means was conducted to investigate whether the speed at which monarchs fly, on average, is faster than the speed at which swallowtails fly. All conditions for inference were met, and the p-value was given as 0.072. Which of the following is a correct interpretation of the p-value?
C. Assuming that monarchs and swallowtails fly at the same speed on average, the probability of observing a difference equal to or greater than the sample difference is 0.072.
Donald believes that western commuters drive an average of 10 miles more per day than eastern commuters do. He selects random samples from each group. The western mean is 23.5 miles, and the eastern mean is 19.4 miles. A 95 percent confidence interval to estimate the difference in population means, in miles, is (2.5,5.7)(2.5,5.7). Which of the following statements is supported by the interval?
C. Donald is likely to be correct because the difference in the sample means (23.5−19.4=4.1) is contained in the interval.
A group of AP Chemistry students debated which fast-food chain had better quality bags, Fast Food Chain W or Fast Food Chain M . They decided to investigate by selecting a random sample of 25 bags from each fast food restaurant, slowly adding water until each bag began to leak, and recording the volume of water they were able to pour into each bag. They then calculated the mean volume and standard deviation, in ounces, for the two types of bags. Which of the following are the correct null and alternative hypotheses to test whether the mean volume of water the bags from Fast Food Chain W can hold without leaking, μW, is different from that for the bags from Fast Food Chain M, μM ?
C. H0:μW−μM=0 Ha:μW−μM≠0
An experiment was conducted to investigate whether there is a difference in mean bag strengths for two different brands of paper sandwich bags. A random sample of 50 bags from each of Brand X and Brand Y was selected. Each bag was held from its rim, and one-ounce weights were dropped into the bag one at a time from the same height until the bag ripped. The number of ounces the bag held before ripping was recorded, and the mean number of ounces for each brand was calculated. Which of the following is the appropriate test for the study?
D. A two-sample t-test for a difference between sample means
Two community service groups, J and K, each have less than 100 members. Members of both groups volunteer each month to participate in a community-wide recycling day. A study was conducted to investigate whether the mean number of days per year of participation was different for the two groups. A random sample of 45 members of group J and a random sample of 32 members of group K were selected. The number of recycling days each selected member participated in for the past 12 months was recorded, and the means for both groups were calculated. A two-sample t-test for a difference in means will be conducted. Which of the following conditions for inference have been met? I. The data were collected using a random method. II. Each sample size is less than 10 percent of the population size. III. Each sample size is large enough to assume normality of the sampling distribution of the difference in sample means.
D. I and III only
A study was conducted to investigate whether the mean numbers of snack bars sold at two airport convenience stores, C and D, were different. For ten randomly selected days, the number of snack bars sold at each store was recorded, and the sample mean number of snack bars for each store was calculated. A two-sample t-test for a difference in means will be conducted. Have all conditions for inference been met?
D. No, the sample sizes are not large enough to assume normality of the sampling distribution.
A two-sample t-test for a difference in means will be conducted to investigate whether the average amount of money spent per customer at Department Store M is different from that at Department Store V. From a random sample of 35 customers at Store M, the average amount spent was $300 with standard deviation $40. From a random sample of 40 customers at Store V, the average amount spent was $290 with standard deviation $35. Assuming a null hypothesis of no difference in population means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (Department Store M minus Department Store V) ?
D. t=300−290/ √40^2/35+35^2/40
A recent newspaper article claimed that more people read Magazine A than read Magazine B. To test the claim, a study was conducted by a publishing representative in which newsstand operators were selected at random and asked how many of each magazine were sold that day. The representative will conduct a hypothesis test to test whether the mean number of magazines of type A the operators sell, μA, is greater than the mean number of magazines of type B the operators sell, μB. What are the correct null and alternative hypotheses for the test?
E. H0:μB−μA=0 Ha:μB−μA>0
Hannah claims that people who live in southern states spend 9 hours more per week outside than do people in northern states. She selects a random sample from each group. The mean number of hours per week that people in southern states spent outside is 18.6, and the mean number of hours per week that people in northern states spent outside is 14.4. A 99 percent confidence interval to estimate the difference in population means (southern minus northern) is (0.4,8.0). Which of the following statements about Hannah's claim is supported by the interval?
E. Hannah is likely to be correct because the difference in the sample means (18.6−14.4=4.2) is contained in the interval.
