stats unit ten review (final)
Researchers are studying the distribution of subscribers to a certain streaming service in different populations. From a random sample of 200 people in City C, 34 were found to subscribe to the streaming service. From a random sample of 200 people in City K, 54 were found to subscribe to the streaming service. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the difference in population proportions (City C minus City K) who subscribe to the streaming service?
1.65 everything over 200
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 sample size greater than 25
Animal 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
Two 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,xL=$113, and 42 people donated to organization M, with an average donation amount of x‾M=$390.xM=$390. What is the correct unit of measure for the mean of the sampling distribution of x‾L−x‾M?xL−xM?
Dollars
Consider a situation in which sampling without replacement is used to generate a random sample from each of two separate populations. To calculate a confidence interval to estimate the difference between population proportions, which of the following checks must be made?
Each population must be at least 10 times as large as its corresponding sample.
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=0.05α=0.05 which of the following is the correct conclusion?
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.
polydactyl cats region a region b
H0:pa−pb=0 Ha:pa−pb>0Ha:pa−pb>0
gardener seeds water germinate 95 percent confidence interval
I and III only
randomized experiments particular drug certain disease anticipated
I, II, and III
Independent random samples of voters from two voting districts, G and H, were selected to investigate the proportion of all voters who favor a proposal to widen a road that runs through both districts. The difference between the sample proportions (G minus H) was used to create the 95 percent confidence interval (0.13, 0.47) for the population difference between districts. Which of the following is the best interpretation of the interval?
It is likely that more voters in district G favor the proposal than in district H, because all values in the interval are positive.
maria two routes commuting to work railroad crossing trains
The p-value is greater than a, and the null hypothesis is not rejected. There is not convincing evidence to support the claim that the proportion of times she needs to stop at the crossing is different for the different routes.
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 of 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?
Yes, all conditions have been met.
A recent study was conducted in which a random sample of men and a random sample of women were surveyed about whether they were fans of a professional football team. The study found that 39 percent of men in the sample were fans and 22 percent of women in the sample were fans. A 99 percent confidence interval for the difference in the proportion of fans of a professional football team between men and women was reported as (0.133, 0.207) Which of the following statements is the best interpretation of the interval?
We are 99% confident that the difference in the population percents of men and women who are fans of a professional football team is between 13.3% and 20.7%
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 inches for the Cherry Fizz soda and 2.1 inches for the Cherry Eclipse soda. A 90 percent confidence interval to estimate the difference in mean diameters, in inches, is ( -0.8, 1.2 ) Which of the following claims is supported by the interval?
Because the interval contains 0, it is possible that there is no difference in mean carbonation levels.
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 for a difference 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?
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.
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,α=0.05, which of the following is a correct conclusion?
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.
There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious apples, 48 had blemishes. In a random sample of 75 of the red delicious apples, 42 had blemishes. Assume all conditions for inference have been met. Which of the following is closest to the interval estimate of the difference in the numbers of apples with blemishes (golden delicious minus red delicious) at a 98 percent level of confidence?
(-105,265)
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 two-sample t-interval for a difference between population means
Two 99 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and W. One confidence interval, I9,I9, will be constructed using samples of size 9 from each of R and W, and the other confidence interval, I81,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 I81I81 will be 1331 the width of I9.I9.
Market researchers interviewed a random sample of 60 men and a random sample of 55 women about their preferences for different color designs for the packaging of a certain product. Of those interviewed, 23 men and 28 women preferred color design X. Which of the following is the correct test statistic for a two-sample z-test for a difference in population proportions for men and women (men minus women) in their preference for color design X ?
z=(0.44)(0.56)(551+601)0.38−0.51
A researcher calculated sample proportions from two independent random samples. Assuming all conditions for inference are met, which of the following is the best method for the researcher to use to estimate the true difference between the population proportions?
Construct a two-sample z-interval for the difference between population proportions.
A political scientist claims that negative advertising on television affects younger voters more than it affects older voters. To test this claim, the scientist obtained data from two random samples of voters categorized into two age-groups, older and younger. The null hypothesis was that there was no difference in the proportions of voters in the two age-groups who would be affected by negative ads. The alternative hypothesis was that the proportion of younger voters affected would be greater than the proportion of older voters affected. Assuming all conditions for inference were met, the scientist conducted the test at a significance level of α=0.05α=0.05. The resulting p-value was 0.206. Which of the following is the correct decision for the test?
The p-value is greater than \(\alpha)\, and the null hypothesis is not rejected. There is not convincing evidence to support the claim that younger voters are more affected by negative ads than are older voters.
Suppose that 25 percent of women and 22 percent of men would answer yes to a particular question. In a simulation, a random sample of 100 women and a random sample of 100 men were selected, and the difference in sample proportions of those who answered yes, p̂women - p̂men, was calculated. The process was repeated 1,000 times. Which of the following is most likely to be a representation of the simulated sampling distribution of the difference between the two sample proportions?
-.20 to .20
To 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, which of the following statements is true?
At the 5% significance level, employees at Site X have a significantly higher mean salary than employees at Site Y do.
A 99 percent confidence interval for a difference in means was given as 25.1±4.3.25.1±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.
A sociologist will conduct a two-sample t-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. With a null hypothesis of no difference in the means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (master's degree minus bachelor's degree) ?
t=284,0002+323,5002(58,000−55,000)
The marketing director for an ice cream company investigated whether there was a difference in preference for two new ice cream flavors—cotton candy and mango. Each participant from a large group of people was randomly assigned to taste one of the two flavors. After tasting, each person rated the flavor on a numerical scale from 1 to 5, where 1 represented strongly dislike and 5 represented strongly like. A two-sample t-interval for a difference between means (cotton candy minus mango) was constructed. Based on the interval, there was convincing statistical evidence of a difference in population mean flavor ratings, with mango having the greater sample mean rating. Which of the following could be the constructed interval?
( -2.1, -1.3 )
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 two-sample t-test for a difference between population means
A two-sample t-test of the hypotheses H0 : μ1 - μ2 = 0 versus Ha : μ1- μ2 > 0 produces a p-value of 0.03. 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.
II and III only
Biologists were studying the proportions of cats that had spotted markings on their fur in two populations of cats, C and F. An independent random sample of cats was taken from each population, and the difference between the sample proportions of cats with the spotted markings (C minus F) was 0.62. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being that the population proportions are not equal. The p-value of the test was 0.01. Which of the following is the correct interpretation of the p-value?
If the proportions of all cats with spotted markings is the same for both populations, the probability of observing a sample difference of at least 0.62 or at most -0.62 is 0.01.
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 percent confidence interval ( 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?
Yes, because 0 is not contained in the interval.
95 percent confidence interval proportion difference supported by the interval
not sufficient evidence
A fitness center piloted two new programs to help people reduce stress levels and maintain a healthy lifestyle. After one month, 112 of the 125 people who volunteered for a program in mindfulness reported a reduction in stress levels, and 110 of the 135 people who volunteered for a yoga program reported a reduction in stress levels. The fitness center wants to investigate whether there is a significant difference between the proportions of all people in the two programs who would report reductions in stress levels. Have the conditions for inference been met?
No, because the samples were not selected or assigned using a random method.
The distribution of ocean wave height at a certain California beach is approximately normal with mean 7.2 feet. The distribution of ocean wave height at a certain Florida beach is approximately normal with mean 6.6 feet. Six waves from each beach will be selected at random and the heights will be recorded. Let x‾CxC represent the sample mean height of the 6 California waves, and let x‾FxFrepresent the sample mean height of the 6 Florida waves. Which of the following is the best interpretation of P(x‾C−x‾F>0.5)=0.55?P(xC−xF>0.5)=0.55?
The probability of observing a difference (California minus Florida) greater than 0.5 feet between the mean height of 6 California waves and the mean height of 6 Florida waves is 0.55.
In the states of Florida and Colorado, veterinarians investigating obesity in dogs obtained random samples of pet medical records and recorded the weights of the dogs in the samples. A test was conducted of H0 : p1 = p2 versus Ha : p1 ≠ p2, where p1 represents the proportion of all overweight dogs in Florida and p2 represents the proportion of all overweight dogs in Colorado. The resulting test statistic for a two-sample z-test for a difference between proportions was 1.85. At the significance level α = 0.05, which of the following is a correct conclusion?
There is not sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is greater than 0.05.
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 two-sample t-test for a difference between population means
Market researchers wanted to know whether the placement of a new product on a supermarket shelf significantly increases the percent of shoppers who will buy the product. At Supermarket X, a new product was placed on the top shelf, and at Supermarket Y, the product was placed one shelf below the top shelf. To observe buying habits, the researchers selected a random sample of 364 shoppers at X and another random sample of 327 shoppers at Y. Of the selected shoppers at X, 15 bought the product, and of the selected shoppers at Y, 19 bought the product. Which of the following is the most appropriate method for analyzing the results?
A two-sample z-test for a difference in population proportions
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 μAμA equal the mean time it took Alice to solve the puzzle cube and μSμSequal 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?
Ho:μA−μS=0 Ha:μA−μS≠0Ha:μA−μS=0
For a population of leghorn chickens, the mean number of eggs laid per chicken is 0.70 with standard deviation 0.20 egg. For a population of Sussex chickens, the mean number of eggs laid per chicken is 0.50 with standard deviation 0.10 egg. Two independent random samples of chickens were taken from the populations. The following table shows the sample statistics. nx‾xsLeghorn360.750.30Sussex360.450.12 Mike claims that for all samples of size 36 from the population of leghorn chickens and all samples of size 36 from the population of Sussex chickens, the mean of all possible differences in sample means (leghorn minus Sussex) is 0.30 eggs per chicken. Is Mike's claim correct?
No. The mean is 0.70 - 0.50 = 0.20 egg per chicken.
A two-sample t-test for a difference in means will be conducted to investigate whether the average length of a cell phone call is shorter this year compared with 5 years ago. From a random sample of 35 phone call records this year, the average length was 25 minutes with a standard deviation of 4 minutes. From a random sample of 32 phone call records from 5 years ago, the average length was 27 minutes with a standard deviation of 5 minutes. The difference (this year minus five years ago) in means will be calculated. With a null hypothesis of no difference in length, which of the following is a correct test statistic for the test?
t=3542+325225−27
To investigate whether there is a significant difference between two regions of a state in the percent of voters who intend to vote for the incumbent governor in the next election, a polling agency interviewed 300 randomly selected voters from the north of the state and 400 randomly selected voters from the south of the state. Of those interviewed, 200 from the north and 325 from the south indicated they intended to vote for the incumbent governor in the next election. Which of the following is the most appropriate method for analyzing the results?
A two-sample z-test for a difference in population proportions