question 11

The producer of a weightloss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.8 pounds with a standard deviation of 1.05 pounds. In a recent study, a group of 45 people who used this pill were interviewed. The study revealed that these people lost a mean of1.77 pounds after one week. If the producer's claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of 45 individuals will be 1.77 pounds or more? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places. xo'? Below are four bivariate data sets and their scatter plots. (Note that all of the scatter plots are displayed with the same scale.) Each data set is made up of sample values drawn from a population. X y V 11- 1.0 3.0 10- 1.0 7.5 10 - 2.0 4.3 9- 2.0 8.6 9-+ X X 3.0 3.2 X X X X 3.0 7.0 X X 4.0 5.1 6- X 4.0 5.5 6- X X X 5.0 4.3 X X 5.0 8.2 X 6.0 7.2 3- X X 5.0 5.4 7.0 6.1 7.0 5.0 8.0 7.5 8.0 6.9 9.0 7.0 + 10 11 9.0 6.0 8 9 10 1 10.0 8.2 Figure 1 10.0 4.4 Figure 21.0 8.3 10 x x 1.0 1.0 10-- x 2.0 4.9 9"x " 2.0 2.0 9\" x S S X 3.0 10.0 3.0 3.0 x 4.0 6.1 6 X * 4.0 4.0 6- x 5.0 2.5 x x 5.0 5.0 x 4 x 4 x 6.0 4.? 3-. x 6.0 6.0 3.. x 10 9.1 2" 10 10 2" x 8.0 3.9 1" w 9.0 9.0 1\"" r 90 g? D ] 2 5 4 5 l5 .7 3 9 1011 90 90 U 1 3 3 4 5 l5 .7 S 9 1011 10.0 6.4 Figure3 10.0 10.0 Figure4 Answer the following questions about the relationships between pairs of variables and the values of r, the sample correlation coefficient. The same response may be the correct answer for more than one question. (a) For which data set is the sample correlation coefficient / closest to 0? (Choose one) (b) Which data set indicates the strongest positive linear relationship between its two variables? (Choose one) (c) Which data set has an apparent negative, but not perfect, linear relationship between its two variables? (Choose one) (d) For which data set is the sample correlation coefficient r equal to 1? ( Choose one)the x, y data set the u, v data set the w, t data set the m, n data set none of the data setsThe lifetime of a certain brand of battery is known to have a standard deviation of 16 hours. Suppose that a random sample of 80 such batteries has a mean lifetime of 42.9 hours. Based on this sample, find a 95% confidence interval for the true mean lifetime of all batteries of this brand. Then give its lower limit and upper limit. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit: X ? Upper limit:Use the ALEKS calculator to solve the following problems. (a) Consider a t distribution with 12 degrees of freedom. Compute P (I i: 1.26). Round your answer to at least three decimal places. P(rl.26)= ] (b) Consider a r distribution with 16 degrees of freedom. Find the value of c such that PIEc 0 020 0=0 0#0An old medical textbook states that the mean sodium level for healthy adults is 138 mEq per liter of blood. A medical researcher believes that, because of modern dietary habits, the mean sodium level for healthy adults, u, now differs from that given in the textbook. A random sample of 90 healthy adults is evaluated. The mean sodium level for the sample is 140 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 11 mEq. Can we conclude, at the 0.05 level of significance, that the population mean adult sodium level differs from that given in the textbook? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H1. O p Ho : 1 X S D O (b) Determine the type of test statistic to use. (Choose one) O=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00(d) Find the Joiiralue. (Round to three or more decimal places.) D (e) Can we conclude that the population mean adult sodium level differs from that given in the textbook? DYes D No Ivanna recently switched her primary doctor to one specializing in caring for elderly patients. On her new doctor's website, it says that the mean systolic blood pressure among elderly females is 115 millimeters of mercury (mmHg). Ivanna believes the value is actually higher. She bases her belief on a recently reported study of 14 randomly selected, elderly females. The sample mean systolic blood pressure was 128 mmHg, and the sample standard deviation was 23 mmHg. Assume that the systolic blood pressures of elderly females are approximately normally distributed. Based on the study, at the 0.10 level of significance, can it be concluded that u, the population mean systolic blood pressure among elderly females, is greater than 115 mmHg? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H. O p Ho : 0 X S (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00A decade-old study found that the proportion, p, of high school seniors who believed that "getting rich" was an important personal goal was 70%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 245 high school seniors in his random sample, 187 believe that "getting rich" is an important goal. Can he conclude, at the 0.10 level of significance, that the proportion has indeed changed? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H. H p Ho : 0 X S H, : 0 (b) Determine the type of test statistic to use. (Choose one) 0=0 050 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) *0 00(d) Find the p-value. (Round to three or more decimal places.) (e) Can it be concluded that the mean systolic blood pressure among elderly females is greater than 115 mmHg? OYes ONo(d) Find the joiiraloe. {Round to three or more decimal places.) D {e} Can we conclude that the proportion of high school seniors who believe that "getting n'ch\" is an important goal has changed? {Pres D No A marriage counselor has traditionally seen that the proportion p of all married couples for whom her communication program can prevent divorce is 80%. After making some recent changes, the marriage counselor now claims that her program can prevent divorce in more than 80% of married couples. In a random sample of 230 married couples who completed her program, 189 of them stayed together. Based on this sample, is there enough evidence to support the marriage counselor's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H,. H O P H : 0 X S p H , : 1 (b) Determine the type of test statistic to use. (Choose one) O=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 070 00{d} Find the pvalue. {Round to three or more decimal places.) D {e} Is there enough evidence to support the marriage counselor's claim that the proportion of married couples for whom her program can prevent divorce is more than 3%? rElites C} No