1) This problem is based on information taken from The Merck Manual (a reference manual used in most medical and nursing schools). Hypertension is defined as a blood pressure reading over 140 mm Hg systolic and/or over 90 mm Hg diastolic. Hypertension, if not corrected, can cause long-term health problems. In the college-age population (18-24 years), about 9.2% have hypertension. Suppose that a blood donor program is taking place in a college dormitory this week (final exams week). Before each student gives blood, the nurse takes a blood pressure reading. Of 193 donors, it is found that 31 have hypertension. Do these data indicate that the population proportion of students with hypertension during final exams week is higher than 9.2%? Use a 10% level of significance. (a) What is the level of significance? b) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? (Please highlight correct answer). H0: p = 0.092; H1: p < 0.092; left-tailed H0: p > 0.092; H1: p = 0.092; right-tailed H0: p = 0.092; H1: p > 0.092; right-tailed H0: p = 0.092; H1: p 0.092; two-tailed (c) What sampling distribution will you use? Do you think the sample size is sufficiently large? The standard normal, since np > 5 and nq > 5. The Student's t, since np > 5 and nq > 5. The standard normal, since np < 5 and nq < 5. The Student's t, since np < 5 and nq < 5. d) What is the value of the sample test statistic? (Use 2 decimal places.) (e) Find the P-value of the test statistic. (Use 4 decimal places.) f) Sketch the sampling distribution and show the area corresponding to the P-value. (g) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? (Please highlight correct answer). At the = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant. At the = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (h) State your conclusion in the context of the application. (Please highlight correct answer). There is sufficient evidence at the 0.10 level to conclude that the true proportion of students with hypertension during final exams week is higher than 0.092. There is insufficient evidence at the 0.10 level to conclude that the true proportion of students with hypertension during final exams week is higher than 0.092. 2) USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 996 Chevrolet owners and found that 491 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to the car company is more than 47%? Use = 0.01. Solve the problem using both the traditional method and the P-value method. Since the pp sampling distribution of is the normal distribution, you can use critical values from the standard normal distribution as shown in the table of critical values of the z distribution. (Round the test statistic and the critical value to two decimal places. Round the P-value to four decimal places.) test statistic = critical value = P-value = a) State your conclusion in context of the application. There is sufficient evidence at the 0.01 level to conclude that the true proportion of consumers loyal to the car company is more than 47%. There is insufficient evidence at the 0.01 level to conclude that the true proportion of consumers loyal to the car company is more than 47%. b) Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? We reject the null hypothesis using the P-value method, but fail to reject using the traditional method. We reject the null hypothesis using the traditional method, but fail to reject using the P-value method. The conclusions obtained by using both methods are the same. 3) How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds): 68 108 134 121 60 64 Assume that the population of x values has an approximately normal distribution. (a) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s. (Round your answers to one decimal place.) x= lb s= lb (b) Find a 75% confidence interval for the population average weight of all adult mountain lions in the specified region. (Round your answers to one decimal place.) lower limit upper limit lb lb 4) For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a marketing survey, a random sample of 732 women shoppers revealed that 628 remained loyal to their favorite supermarket during the past year (i.e., did not switch stores). (a) Let p represent the proportion of all women shoppers who remain loyal to their favorite supermarket. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 95% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit c) Give a brief explanation of the meaning of the interval. 5% of all confidence intervals would include the true proportion of loyal women shoppers. 5% of the confidence intervals created using this method would include the true proportion of loyal women shoppers. 95% of all confidence intervals would include the true proportion of loyal women shoppers. 95% of the confidence intervals created using this method would include the true proportion of loyal women shoppers. (d) As a news writer, how would you report the survey results regarding the percentage of women supermarket shoppers who remained loyal to their favorite supermarket during the past year? Report pp along with the margin of error. Report the margin of error. Report the confidence interval. Report pp . e) What is the margin of error based on a 95% confidence interval? (Round your answer to three decimal places.) 5) The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr). Predictor Coef SE Coef T P Constant 0.8300 0.4148 2.06 0.84 Weight 0.38621 0.02978 13.52 0.000 S = 0.517508 RSq = 96.0% (a) Write out the least-squares equation. = + x (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.) (c) What is the value of the correlation coefficient r? (Use 3 decimal places.)