Flashcards
Unit 13 - Inference with Two Sample Means Test
Flashcards do conjunto (25)
- 1An amateur men’s swimming association is trying to decide whether times in the 100-meter breaststroke will be reduced if the men shave their heads. From the population of swimmers, six were selected at random and agreed to swim two races—one before shaving their heads and one after shaving their heads. The results for each race, with times in seconds, are given in the table below. Let µ1 represent the population mean of swimming times before shaving and µ2 represent the population mean of swimming times after shaving. Let µd represent the population mean of the differences, X1 - X2. These differences follow a normal distribution. Which of the following would be the most appropriate test and alternative hypothesis to use in testing this theory?A paired t-test with Ha : µd > 0
- 2Suppose the mean in trunk diameter of the giant sequoia tree species is 15.7m, while the mean in trunk diameter of the California redwood tree species is 10.6m. Let 1 represent the average trunk diameter of four randomly sampled giant sequoia trees, and let 2 represent the average trunk diameter of three randomly sampled California redwood trees. If the random sampling is done with replacement, what is the mean of the sampling distribution of the difference in sample means?5.1 m
- 3A biologist studied the frequency of croaks for frogs from two different regions. From a random sample of 32 frogs located in the northern region, the mean number of croaks per hour was 21.3, and from a random sample of 38 frogs located in the southern region, the mean number of croaks per hour was 28.9. To estimate the difference in the mean number of croaks (southern minus northern), a 95 percent confidence interval was constructed from the samples. The interval was reported as (7.1,8.1). Which of the following claims is supported by the interval?The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.
- 4Two 99 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and W. One confidence interval, I9, will be constructed using samples of size 9 from each of R and W, and the other confidence interval, I81, will be constructed using samples of size 81 from each of R and W. When all other things remain the same, which of the following describes the relationship between the two confidence intervals?The width of I81 will be 13 the width of I9 .
- 5A team of psychologists studied the effect of multitasking on the completion of cognitive tasks. A group of 40 women participated in the study. Each woman owned a smartphone equipped with the same type of keyboard. The women typed a text passage on the phone twice, one time while sitting in a quiet room (a single task) and the other time while walking (a multitask). The order of the single task and the multitask was randomly determined for each woman. The psychologists recorded the time it took each woman to type the text for both tasks. If the conditions of inference are met, which of the following tests is most appropriate to analyze the data?A matched-pairs t-test for a mean difference
- 6A sociologist will conduct a two-sample -test for a difference in means to investigate whether there is a significant difference, on average, between the salaries of people with bachelor’s degrees and people with master’s degrees. From a random sample of 32 people with a bachelor’s degree, the average salary was $55,000 with standard deviation $3,500. From a random sample of 28 people with a master’s degree, the average salary was $58,000 with a standard deviation of $4,000. Assuming conditions have been met, with a null hypothesis of no difference in the means, which of the following is the approximate p-value for the appropriate test to investigate whether there is a difference in population means (master’s degree minus bachelor’s degree)?0.0033
- 7A two-sample t-test of the hypotheses H0 : μ1 - μ2 = 0 versus Ha : μ1- μ2 > 0 produces a p-value of 0.02. Which of the following must be true? I. A 90 percent confidence interval for the difference in means will contain the value 0. II. A 95 percent confidence interval for the difference in means will contain the value 0. III. A 99 percent confidence interval for the difference in means will contain the value 0.III only
- 8In a random sample of 60 shoppers chosen from the shoppers at a large suburban mall, 36 indicated that they had been to a movie in the past month. In an independent random sample of 50 shoppers chosen from the shoppers in a large downtown shopping area, 31 indicated that they had been to a movie in the past month. What significance test should be used to determine whether these data provide sufficient evidence to reject the hypothesis that the proportion of shoppers at the suburban mall who had been to a movie in the past month is the same as the proportion of shoppers in the large downtown shopping area who had been to a movie in the past month?Two proportion z-test
- 9Hannah 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.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. - 10A state educational agency was concerned that the salaries of public school teachers in one region of the state,region A, were higher than the salaries in another region of the state, region B. The agency took two independent random samples of salaries of public school teachers, one from region A and one from region B. The data are summarized in the table below. Assuming all conditions for inference are met, do the data provide convincing statistical evidence that the salaries of public school teachers in region A are, on average, greater than the salaries of public school teachers in region B?Yes, there is evidence at the significance level of α = 0.05 but not at α = 0.01.
- 11A biologist wants to estimate the difference between the mean body lengths of green and brown stinkbugs. A random sample of 20 green stinkbugs has a mean body length of 16.22 millimeters (mm) and a standard deviation of 1.34 mm. A random sample of 20 brown stinkbugs has a mean body length of 13.41 mm and a standard deviation of 0.73 mm. Assuming all conditions for inference are met, what is a 95 percent confidence interval for the difference (green - brown) between the sample means?(2.1125, 3.5075)
- 12A reporter responsible for the food section of a magazine investigated the belief that grocery stores sell beef at a lower 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 represents the mean price of beef in the spring?Ho: µF = µS Ha: µF < µS
- 13Animal researchers studying cows and horses conducted a two-sample t-test for a difference 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 a p-value of 0.0487. Which of the following is a correct interpretation of the p-value?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.
- 14Frank, who lives in Texas, and his sister Lilly, who lives in Japan, correspond regularly. From what he can tell from the postmarks on both his and his sister’s letters, it appears that it takes longer for Lilly’s mail from Japan to reach him in Texas than it does for his letters from Texas to reach her in Japan. When Frank called his post office to ask if there was a reason for this, the postmaster told him that the delivery time of letters in both directions should be the same. Frank and his sister decided to collect data to see if letters from Japan to Texas take longer to be delivered than letters from Texas to Japan. They recorded the delivery time in days. After convincing themselves that the assumptions were reasonable, they performed a two-sample t-test and obtained the following computer output. Using a significance level of 0.05, which of the following statements best describes the conclusion that can be drawn from these data?There is not convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan.
- 15A statistics student wants to compare the mean times needed to access flight information for two major airlines. Twenty randomly selected students accessed one airline's Web site, and the time required to locate the flight information using the Web site had a mean of 2.4 minutes and a standard deviation of 0.7 minute. Twenty different randomly selected students accessed the other airline's Web site, and the time required to locate the flight information using the Web site had a mean of 2.1 minutes and a standard deviation of 0.3 minutes. Assuming that the conditions for inference are met, which of the following statements about the p-value obtained from the data and the conclusion of the significance test is true?The p-value is greater than 0.05 but less than 0.10; therefore at the 0.10 level, there is a significant difference in mean search times on the two Web sites.
- 16The management of a large hardware store is interested in estimating the difference between the mean dollar amount of purchases made by customers who use the store’s credit card and the mean dollar amount of purchases made by customers who use a different credit card. A random sample of 74 customers who used the store’s credit card showed a mean purchase of $107 with a standard deviation of $12. A separate random sample of 58 customers who used a different credit card showed a mean purchase of $132 with a standard deviation of $9. Technology was used to calculate that the correct number of degrees of freedom is 129.78. Which of the following represents the margin of error for a 98 percent confidence interval to estimate the difference in the mean purchase amount for the two types of credit cards?
- 17A matched-pairs t-test is NOT an appropriate way to analyze data consisting of which of the following?Measurements of annual income for both individuals in pairs formed by assigning 100 people to pairs at random
- 18A 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?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. - 19A large school district held a district-wide track meet for all high school students. For the 2-mile run, the population of female students participating had a mean running time of 8.8 minutes with standard deviation of 3.3 minutes, and the population of male students participating had a mean running time 7.3 minutes with standard deviation of 2.9 minutes. Suppose 8 female students and 8 male students who participated in the 2-mile run are selected at random from each population. Let x¯F represent the sample mean running time for the female students, and let x¯M represent the sample mean running time for the male students. What are the mean and standard deviation of the sampling distribution of the difference in sample means x¯F−x¯M ?
- 20To determine whether employees at Site X have higher salaries, on average, than employees at Site Y of the same company do, independent random samples of salaries were obtained for the two groups. The data are summarized below. Based on the data what is the degrees of freedom for a two sample t inference procedure?415
- 21A fair six-sided die, with sides numbered 1 through 6, will be rolled a total of 15 times. Let represent the standard deviation of the first ten rolls, and let represent the standard deviation of the remaining five rolls. What is the standard deviation of the sampling distribution of the difference in sample means?
- 22Makers of a new pain-relieving medication claim that it relieves chronic pain faster than the current top-selling pain reliever on the market. A double-blind experiment was conducted in which 10 people who experience chronic pain were randomly selected to take either the new or the current medication. Each of the 10 people recorded the time, in minutes, from taking the medication until pain relief. After an appropriate time period, each of the 10 people took the other medication and recorded the time from taking the medication until pain relief. The medication each person took first was randomly determined, and because both medications look the same, the people in the study did not know which medication was taken first. The table below shows summary statistics for the results. Which of the following values is closest to the p-value of the appropriate t-test?0.1802
- 23Two non-profit organizations, L and M, accept donations from people. In a certain month, 140 people donated to organization L, with an average donation amount of x¯L=$113, and 42 people donated to organization M, with an average donation amount of x¯M=$390. What is the correct unit of measure for the mean of the sampling distribution of x¯L−x¯M?Dollars
The unit for the mean of the sampling distribution of x¯L−x¯M is the same as the unit for the individual sample means, which is dollars. - 24Carol wants to know if there is a difference in the mean price between to brands of hair products. From Brand A, she selected and analyzed a random sample of 35 different products, and from Brand B selected and analyzed a random sample of 43 different products. Carol observed that in a graphed boxplot for Brand B displayed two outliers. Carol wants to run a hypothesis test to determine if there is a difference in the population means. Is the sampling distribution of the difference in sample means approximately normal?Yes, because the size of each sample is at least 30.
- 25A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?
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- 10th grade Math FlashCards sobre Unit 13 - Inference with Two Sample Means Test, criado por Kelly Chen em 02-05-2021.
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- Kelly Chen
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