Which test is it?
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. One-ounce weights were dropped into each 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?
A. A matched-pairs t-test for a mean difference
B. A two-sample t-test for a difference between population means
C. A two-sample z-test for a difference between population proportions
B. A two-sample t-test for a difference between population means
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 p-value and a significance level of α=0.02, what is the correct conclusion (is there convincing statistical evidence?)
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 95% confidence interval for the difference in mean response times (urban – rural) for two emergency service districts is (-1.8 minutes, 0.4 minutes). Which of the following is the most appropriate conclusion?
A. The urban district has a significantly faster mean response time.
B. The rural district has a significantly faster mean response time.
C. There is no significant difference between the population mean response times.
C. There is no significant difference between the population mean response times.
When constructing a 99% confidence interval for a population mean with a sample size of 25, why is the critical value t* = 2.797 used instead of the z-score 2.576?
A. The t-distribution provides a narrower interval
B. The t-distribution accounts for additional variability when σ is unknown
C. The sample size is too small to use a z-score
B. The t-distribution accounts for additional variability when σ is unknown
Researchers calculated a 90% confidence interval for the difference in mean wait times (clinic A – clinic B) as (-5.2 minutes, -1.8 minutes). What is the correct interpretation of this interval?
We are 90% confident that clinic B's mean wait time exceeds clinic A's by 1.8 to 5.2 minutes.
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?
A. A one-sample t-test for a population mean
B. A two-sample t-test for a difference between sample means
C. A two-sample t-test for a difference between population means
D. A two-sample t-test for a difference between population means
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. What is a correct interpretation of the p-value?
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.
A two-sample t-test will be conducted to investigate whether the mean number of tickets sold 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 tickets with standard deviation 12. From a random sample of 60 days at theater K, the average was 85 tickets with standard deviation 14. what is the appropriate test statistic for the test?
t= (75-85)/ sqrt (12^2/50 + 14^2/60)
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?
No, the sample sizes are not large enough to assume normality of the sampling distribution.
A certain ambulance service wants its average time to transport a patient to the hospital to be 10 minutes. A random sample of 12 transports yielded a 95 percent confidence interval of 11.8±1.6 minutes. Is the claim that the ambulance service takes an average of 10 minutes to transport a patient to the hospital plausible based on the interval?
The claim is not plausible because 10 falls outside of the interval.
A marketing executive is investigating whether this year's advertising campaign has resulted in greater mean sales compared with last year's mean sales. The executive collects a random sample of 100 customer orders from a large population of orders and calculates the sample mean and sample standard deviation. What is the appropriate test for the executive's investigation?
A one-sample t-test for a population mean
Students debated which fast-food chain had better quality bags, Fast Food Chain W or 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 for the two types of bags. What is 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 ?
Ho: μW- μM=0
Ha: μW- μM≠0
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 Store M is different from that at 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. What is the test statistic for the appropriate test to investigate whether there is a difference in population means (Store M minus Store V) ?
t= (300-290)/ sqrt (40^2/35 + 35^2/40)
A researcher studying the sleep habits of teens will select a random sample of n teens from the population to survey. The researcher will construct a t-interval to estimate the mean number of hours of sleep that teens in the population get each night. Which of the following is true about the t-distribution as the value of n decreases from 40 to 20 ?
A. The center remains constant, and the area in the tails of the distribution remains constant.
B. The center remains constant, and the area in the tails of the distribution decreases.
C. The center remains constant, and the area in the tails of the distribution increases.
D. The center remains constant, and the area in the tails of the distribution increases.
A strategy was designed to limit elk from crossing a field is to surround the field with a fence. Some elk, however, will still be able to bypass the fence. For a period of one month, the number of elk found crossing a sample of fields with a fence was recorded and used to construct the 95 percent confidence interval (2.9,4.4) for the mean number of elk. The interval provides convincing statistical evidence for which of the following claims
A. The mean number of elk to cross a field protected by a fence is 4 per month.
B. The mean number of elk to cross a field protected by a fence is 2 per month.
C. The mean number of elk to cross all fields protected by a fence is greater than 2 per month.
C. The mean number of elk to cross all fields protected by a fence is greater than 2 per month.
To study the effectiveness of an adult reading program, researchers will select a random sample of adults who are eligible for the program. The selected adults will be given a pretest before the program and a posttest after the program. The difference in the number of correct answers on the pretest and the number of correct answers on the posttest will be recorded for each adult in the sample. Which of the following is the most appropriate inference procedure for the researchers to use to analyze the results?
A. A one-sample z-interval for a population proportion
B. A one-sample t-interval for a sample mean difference
C. A matched-pairs t-interval for a population mean difference
C. A matched-pairs t-interval for a population mean difference
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?
Ho: μA- μB=0
Ha: μA- μB>0
The mean and standard deviation of a random sample of 7 baby orca whales were calculated as 430 pounds and 26.9 pounds, respectively. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the mean weight of all baby orca whales?
430 ± 1943(26.9/√7)
Two community service groups, J and K, volunteer each month to participate in a 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?
1 and 3 only
Sociologists studying the behavior of high school freshmen in a certain state collected data from a random sample of freshmen in the population. They constructed the 90 percent confidence interval 6.46±0.41 for the mean number of hours per week spent by freshmen in extracurricular activities. Assuming all conditions for inference are met, what is a correct interpretation of the interval?
We are 90 percent confident that the mean number of hours spent in extracurricular activities for freshmen in the state is between 6.05 hours and 6.87 hours per week.
A sociologist wants to estimate the average total number of minutes spent on social media per day in the population. A random sample of 50 high school students was selected, and they were asked, “How many minutes per day, on average, do you spend visiting social media sites?"Which of the following is the most appropriate inference procedure for the sociologist to use?
A. A one-sample z-interval for a population proportion
B. A one-sample t-interval for a population mean
C. A matched-pairs t-interval for a mean difference
B. A one-sample t-interval for a population mean
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. What is a correct interpretation of the p-value?
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.
A recent study of 1,215 randomly selected middle school students revealed that the average number of minutes they spent completing homework during the school week was 180 minutes with a standard deviation of 45 minutes. Which of the following is the standard error, in minutes, of the sampling distribution of the mean number of minutes spent on homework per week for all middle school students?
4/√ (1,215)
A counselor, at a high school of 500 students, wants to estimate the mean number of hours per week that students at the school spend in community service activities. The counselor will survey 20 students in the Environmental Club at the school. The mean number of hours for the 20 students will be used to estimate the population mean.
Which of the following conditions for inference have not been met?
1 and 2 only
A linguist at a large university was studying the word length of papers submitted by students enrolled in humanities programs. From a random sample of 25 papers, the linguist counted the number of words used in each paper. The 95 percent confidence interval was calculated to be (20,995, 22,905). Assuming all conditions for inference are met, what is a correct interpretation of the interval?
We are 95 percent confident that the mean word length for all papers submitted by students in humanities programs is between 20,995 words and 22,905 words.