# STATS Assignment 2016

1. The 95% confidence interval for the mean height of all World Campus STAT 200 students is 66.914 inches to 67.633 inches. If all other factors are held constant, how would the width of the interval change if you constructed a 90% confidence interval? A) The width would be decreased (i.e., it would be more narrow). B) The width would be unchanged. C) The width would be increased (i.e., it would be wider). Review 2. According to the CDC, adults should exercise at least 2.5 hours per week. In Spring 2016 data were collected from a random sample of 522 World Campus students. A 95% confidence interval for the mean number of hours exercised per week was computed to be [3.7903, 4.6426]. Is there evidence that the mean number of hours exercised by World Campus students per week is greater than the CDC’s recommendation of 2.5 hours? A) Yes, there is evidence that the mean number of hours exercised by World Campus students per week is greater than 2.5 hours. B) No, there is not evidence that the mean number of hours exercised by World Campus students per week is greater than 2.5 hours. Review 3. Which of the following statements is true about a parameter and a statistic for samples taken from the same population? A) The value of the parameter varies from sample to sample. B) The value of the statistic varies from sample to sample. C) Both A and B are true. D) Neither A nor B is true. Review 4. Suppose that length of hospital stays are independent and normally distributed with an average stay of 6.3 days and standard deviation of 2.5 days. What is the standard deviation of the distribution of sample means (i.e., standard error) for random samples of n = 100 patients? A) 0.630 days B) 0.025 days C) 0.063 days D) 0.250 days Review 5. In Spring 2016 data concerning shoe size were collected from a sample of 287 female World Campus students. In that sample, the mean shoe size was 7.977 with a standard deviation of 1.317. According to Minitab, the standard error of the mean is 0.0777. Which of the following interpretations of this standard error of the mean is correct? A) In this sample of n=287 the standard deviation for individual shoe sizes was 0.0777 B) In the population of all female World Campus students, the standard deviation of their shoe sizes is estimated to be 0.0777 C) If we were to repeatedly pull samples of n=287 from the population of all female World Campus students and record each sample’s mean, we could create a distribution of sample means that would have an estimated standard deviation of 0.0777 Review 6. In Fall 2015 data were collected from a sample of 402 World Campus students concerning their residency. In the sample of n=402, the proportion who were Pennsylvania residents was computed to be .433 What is the ?argin of error ?mfor the 95% confidence interval of the population proportion? Hint: For a 95% confidence interval of a proportion, z* = 1.96 A) .0006 B) .0247 C) .0484 D) .0969 Review 7. When the 2000 General Social Survey asked participants if they would be willing to accept cuts in their standard of living to protect the environment, 350 of 1400 participants responded “yes.” Construct a ? confidence interval for the proportion of all Americans who would accept cuts in their 98% ?standard of living to protect the environment. Hint: For a 98% confidence interval of a proportion z* = 2.33 A) (0.2309, 0.2691) B) (0.2273, 0.2727) C) (0.2230, 0.2770) D) (0.2201, 0.2799) Review 8. A randomly selected sample of n = 101 12 oz size bottles of energy drinks contained an average of 11.68 oz of content with a standard deviation of 0.3 oz. Calculate a 95% confidence interval for the mean amount of content for such bottles. Hint: For a 95% confidence interval with 100 degrees of freedom t* = 1.984 A) (11.62, 11.74) B) (11.65, 11.71) C) (11.45, 11.91) D) (11.38, 11.98) Review 9. A bakery wants to estimate the proportion of its customers who like red velvet cupcakes because they do not know the value of the proportion. In order to construct a 95% confidence interval with a margin of error of .05, what is the minimum sample size that they should obtain? Hint: For a 95% confidence interval for a proportion, z* = 1.96 A) 1921 B) 385 C) 196 D) 39 Review 10. A random sample of 100 residents in a town was take to determine if more than half of all town residents approve of the current mayor. Using p to represent the population proportion of resident approval, is the hypothesis statement p ? 0.5 the null hypothesis or the alternative hypothesis? A) Null hypothesis B) Alternative hypothesis Review 11. A hypothesis test is done in which the alternative hypothesis states that less than 50% of residents of a town approve of the current mayor. The level of significance for the test is 0.05. The pvalue for the test is 0.031. Which of the following conclusions is accurate? A) We ? conclude that ?ore than 50%?can ?m of the population approves of the current mayor. B) We ? conclude that?can ? less than 50%? of the population approves of the current mayor. C) We ? conclude that ?can ?exactly 50%? of the population approves of the current mayor. D) We ?cannot ?conclude that? less than 50%? of the population approves of the current mayor. Review 12. A ?test statistic? is A) the sample mean. B) the number of observations in a sample. C) a value calculated from the data in the sample used to decide between the null and alternative hypotheses. D) a confidence interval. Review 13. In Fall 2015 data concerning pet ownership were collected from a sample of 402 World Campus students. We want to know if the average number of pets owned by World Campus students is greater than 1 in the population of all World Campus students. Given the output above, which of the following conclusions is correct at the .05 ? level? A) ?Fail to reject? the null hypothesis, there ?is evidence? that the mean number of pets owned by World Campus students is greater than 1. B) ?Fail to reject? the null hypothesis, there ?is NOT evidence? that the mean number of pets owned by World Campus students is greater than 1. C) ?Reject? the null hypothesis, there ?is NOT evidence? that the mean number of pets owned by World Campus students is greater than 1. D) ?Reject? the null hypothesis, there ?is evidence? that the mean number of pets owned by World Campus students is greater than 1. Review 14. Is there evidence that the population proportion is different from 50%? Given the Minitab output above, which of the following conclusions is correct? A) ?Reject? the null hypothesis, there ?is evidence? that the population proportion is different from 50%. B) ?Reject? the null hypothesis, there ?is NOT evidence? that the population proportion is different from 50%. C) ?Fail to reject? the null hypothesis, there ?is evidence? that the population proportion is different from 50%. D) ?Fail to reject? the null hypothesis, there ?is NOT evidence? that the population proportion is different from 50%. Review 15. An inspector at a company that produces fiberboard wants to test a sample of products to determine if quality standards are being met. The inspector collects a random sample of 44 units and measures the strength to determine whether the mean strength exceeds 18 MPa. The sample mean for the intermediary units is 20.42 MPa. The sample standard deviation is 9 MPa. What is the value of the test statistic? A) t = 0.27 B) t = 0.27 C) t = 1.78 D) t = 1.78 Review 16. Research question:? Is the mean engine size (in liters) different for cars that are two wheel drive versus all wheel drive? A sample of 93 cars was examined. A ttest statistic of 0.31 with 91 degrees of freedom was computed along with a corresponding pvalue of 0.7544 If, in reality, there is a difference in the mean engine sizes of two wheel drive and all wheel drive cars, what type of error was made here? A) Type I error B) Type II error Review 17. Research question:? Do residents of Belgium and residents of Germany have ?different ?heights on average? ?b?? = mean height in residents of Belgium ?g?? = mean height in residents of Germany Which of the following sets of hypotheses should be used to test this research question? A) H? ? ?: ? ?g? ? 0 0? b?Ha? b? g?? ? ?: ? ? = 0 B) H0? b? g?? ? ?: ? ? = 0 H? ? ?: ?b? g?a? ? ? 0 C) H? ? ?: ? ?g? > 0 0? b?Ha? b? g?? ? ?: ? ? ? 0 D) H? ? ?: ? ?g? ? 0 0? b?H? ? ?: ?b? g? ? > 0 a? Review 18. During a fitness study, researchers monitor water lost during a particular exercise routine as a measure of fitness. The mean change in water loss should be at least 50 mg in order to represent a change in fitness level. In a sample of 31 participants, they find a mean change of 34 mg with a standard deviation of 14 mg. What is the value of the test statistic? A) t = 6.36 B) t = 6.36 C) t = 1.14 D) t = 1.14 Review 19. In 1993 a researcher collected data concerning 93 new car models. You want to know if the fuel tank capacity (in gallons) is different for cars that are and are not avaliable with manual transmission. Given the output above, what is the correct conclusion? A) ?Reject? the null hypothesis, there ?is evidence? that the mean fuel capacity (in gallons) is different for cars that are and are not available with manual transmission. B) ?Fail to reject? the null hypothesis, there ?is evidence? that the mean fuel capacity (in gallons) is different for cars that are and are not available with manual transmission. C) ?Fail to reject? the null hypothesis, there ?is NOT evidence? that the mean fuel capacity (in gallons) is different for cars that are and are not available with manual transmission. D) ?Reject? the null hypothesis, there ?is NOT evidence? that the mean fuel capacity (in gallons) isdifferent for cars that are and are not available with manual transmission. Review 20. Research question?: Is the proportion of World Campus students who own a dog different for Pennsylvania and nonPennsylvania residents? In Spring 2016 data were collected from 522 World Campus students concerning their dog ownership and state residency. Given the Minitab output above, which of the following conclusions is correct? A) ?Reject? the null hypothesis, there ?is evidence? that the proportion of Pennsylvania and nonPennsylvania residents who own a dog is different. B) ?Reject? the null hypothesis,there ?is NOT evidence? that the proportion of Pennsylvania and nonPennsylvania residents who own a dog is different. C) ?Fail to reject? the null hypothesis, there ?is evidence? that the proportion of Pennsylvania and nonPennsylvania residents who own a dog is different. D) ?Fail to reject? the null hypothesis, there ?is NOT evidence? that the proportion of Pennsylvania and nonPennsylvania residents who own a dog is different. Review 21. Machine Sample Size Mean Standard Deviation A 30 12.1 tons 6.2 B 30 10.9 tons 4.9 C 30 11.5 tons 7.5 D 30 13.0 tons 13.3 Four different machines (A, B, C, and D) are being considered for use in manufacturing rubber seals. The machines are being compared with respect to the tensile strength of the product. A random sample of 30 seals from each machine is used to determine whether or not the mean tensile strength varies from machine to machine. Based on the above output comparing the mean tensile strength of the products for each machine a oneway analysis of variance (i.e., Ftest) A) should ? be done because the sample means are unequal. not?B) should ? be done because the sample standard deviations differ by so much. not ?C) can be done because the sample means are unequal. D) can be done because the sample sizes are all equal. Review 22. When a oneway analysis of variance test is done, what probability distribution is used to find the pvalue? A) Normal distribution (i.e., z distribution) B) Fdistribution C) tdistribution D) Chi square distribution Review 23. A farmer wanted to test whether there was a difference in the average corn yield for 4 different fertilizer. He divides his field into 20 sub plots and randomly assigns 5 plots to each fertilizer. What is the ?null hypothesis? for this situation? A) The average corn yield for all four fertilizers is not the same. B) The average corn yield for all four fertilizers is the same. C) The average corn yield for each of the 20 sub plots is not the same. D) The average corn yield for each of the 20 sub plots is the same. Review 24. A study compared the number of hours spent weekly studying for students grouped by their preferred seat position in class (back, middle, front). The pvalue for the Ftest and degrees of freedom for the grouping variable are given in the Analysis of Variance table above. Given an alpha level of 0.05, what is the conclusion from the analysis of variance? A) The null hypothesis is rejected: the population means are all equal B) The null hypothesis is not rejected: the population means are all equal C) The null hypothesis is rejected: at least two of the population means differ D) The null hypothesis is not rejected: at least two of the population means differ E) Review 25. In 1993 a researcher collected data concerning 93 new car models. He wants to know what kind of drive train results in the highest highway miles per gallon (MPG): all wheel drive, front wheel drive, or rear wheel drive. He conducted a oneway ANOVA and found that F(2, 90) = 6.28, p = .0028 Below are the results of his posthoc analyses. Given the Minitab Express output above, which of the following pairs are significantly different from one another? A) Front Wheel Drive and Rear Wheel Drive B) Front Wheel Drive and All Wheel Drive C) Rear Wheel Drive and All Wheel Drive Review 26. A team of counselors wants to compare the average anxiety levels of college students who take an exam while petting a dog, a cat, or a teddy bear. They take a random sample of 90 college students and randomly assign 30 students to pet a dog, 30 students to pet a cat, and 30 students to pet a teddy bear. They measure each participant’s anxiety levels while taking an exam. Which of the following hypothesis testing procedures is appropriate given this scenario? A) Oneway analysis of variance B) Single sample t test for a mean C) Independent t test D) Paired (dependent) t test Review 27. The human resources department at a large hotel wants to compare three methods of providing sexual harassment training to their employees: online training, hybrid training, and facetoface training. They take a random sample of 90 employees and randomly assigned 30 to receive online training, 30 to receive hybrid training, and 30 to receive facetoface training. At the end of the training program they measure the employees’ knowledge of sexual harassment policies and reporting procedures. Which of the following hypothesis testing procedures is appropriate given this scenario? A) Oneway analysis of variance B) Single sample t test for a mean C) Independent t test D) Paired (dependent) t test Review 28. Research question:? Do cars manufactured in the United States tend to have higher passenger capacities than cars manufactured outside of the United States? Passenger capacity is the number of people that can comfortably be seated in the car. Which of the following hypothesis tests would you use to answer this research question? A) Two sample proportion z test B) Two independent means t test C) One sample mean t test D) One sample proportion z test Review 29. Which of the following is ?TRUE ?about hypothesis testing? A) In hypothesis testing, sample statistics are used to make inferences about population parameters. B) Hypotheses are statements about the sample(s). C) The alternative hypothesis always contains an equality. D) Results are said to be statistically significant when the p value is greater than the alpha level. Review 30. If we “fail to reject” the null hypothesis, that means that the null hypothesis must be true. A) True B) False Review 31. Research question:? Do World Campus and University Park students differ in terms of typical age? The data:? A sample of 200 World Campus and 200 University Park students were surveyed and asked how old they were (in years). A) What hypothesis test would you use to address this research question and ?HY?W ? B) What graph would you use to display this data and ?HY?W ? HTML Editor Review 32. A STAT200 instructor wanted to know if students’ scores were different on the midterm 2 and final exams. A paired means ttest was conducted. Descriptive statsitics are presented in the following table: With 215 degrees of freedom the t test statisitc was 2.225 with a corresponding pvalue of .027 The instructor reported, “Given t(215)=2.225, p=.027, I find that there is not evidence that students scored differently on the two exams. In response to these findings I suggest that we do not give students midterm exams. There is no new information gained from giving students midterm exams when their final exam scores are the same. Instead, all exam points should come from their final exam alone.” Describe two things that are wrong with this interpretation. HTML Editor Review 33. For the 50 U.S. states, it is found that participation rate (X) can explain 76.5% of the variation in average SAT score (Y). The higher the participation rate, the lower the average SAT score. What is the correlation between X and Y? A) 0.875 B) 0.875 C) 0.585 D) 0.585 Review 34. Assume the correlation between Height (measured in inches) and Weight (measured in pounds) was found to be ?r? = 0.75. If Height were changed to being measured in centimeters (where 1 inch = 2.54 centimeters) what effect would this have on the correlation? A) The correlation would remain the same. B) The correlation would increase by 0.75 times 2.54 C) The correlation would decrease by 0.75 divided by 2.54 Review 35. The regression line for a set of points is given by y = 51 8x. What is the estimated yintercept of the line? A) 51 B) 8 C) 8 D) 51 Review 36. A regression between annual advertising expenditure (explanatory variable in Million dollars) and annual sales (response variable in Million dollars) for 300 companies resulted in the following regression equation: Y = 42.16 + 0.015X One company in the sample has a 3 million dollar advertising budget. What are the predicted sales for this company? A) 42.205 million dollars B) 38.026 million dollars C) 59.487 million dollars D) 57.329 million dollars Review 37. A regression was done to study the relationship between X=yearly income (in thousands of dollars per year) of home purchaser and Y=sale price of the house (in thousands of dollars). These 3,000 households have yearly income ranging from 25 to 70 thousands of dollars. The regression equation is: y = 47.2 + 1.799x A home purchaser earns $450,000 annually. What is the problem with using this regression equation to estimate the sale price of the house for this person? A) The regression equation is based on 3,000 households with the highest yearly income being $70,000. B) No problem with using this regression equation. Review 38. Which of the following is the strongest of the possible Rsquared values? A) 64% B) 0% C) 80% D) 150% Review 39. A group of kinesiology students want to know if, on average, kinesiology majors can run a mile in less than 9 minutes. They take a random sample of 25 students and record the amount of time it takes them to run a mile. Which of the following hypothesis testing procedures is appropriate given this scenario? A) Single sample t test for a mean B) Single sample z test for a proportion C) Independent t test D) Simple linear regression Review 40. There is a known linear relationship between hours spent studying and scores on a midterm exam. The instructor of that course wants to use hours spent studying to predict midterm exam scores. What statistical procedure is appropriate given this scenario? A) Simple linear regression B) Paired (dependent) t test C) Chisquare test of independence D) Independent t test