PHST 301 Homework 6: 20 points Due: 11/20/23 11:59 PM 1) (5 points) A group of 21 adults volunteered for a fitness study to examine whether an aerobics program can lower the resting heart rate of an average adult. Test the hypothesis that individuals participating in an aerobics program have lower resting heart rates than the national average. Let =0.05. a) (0.5 points) What is the outcome variable? Is this outcome variable considered to be continuous or dichotomous? b) (1 point) Set up the appropriate null and alternative hypotheses. You may assume that the average resting heart rate of adults in the U.S. is 73.0 beats/minute. c) (1 point) Select the appropriate test statistic. Should a z or t test statistic be used for this hypothesis test? Explain your reasoning and/or show your work. d) (0.5 points) Write out the decision rule for this hypothesis test. Make sure to include the appropriate z or t critical value. e) (1 point) After nine months, the mean resting heart rate for the participants in the aerobics fitness program was 69.4 beats/minute with a standard deviation of 6.2. Use this information to calculate the appropriate test statistic. Show your work. f) (1 point) Make a decision using the decision rule in (d) and the calculated test statistic in (e). Write out an appropriate conclusion. 2) (4 points) Reports have shown that the proportion of deaths due to cancer in the U.S. is 20%. A researcher wants to examine whether workers in U.S. nuclear power plants have an increased proportion of deaths due to cancer compared to the national average. A hypothesis test was conducted at a 5% significance level. a) (0.5 points) What is the outcome variable? Is this outcome variable considered to be continuous or dichotomous? b) (1 point) State the null and alternative hypotheses used in this study. c) (1.5 points) During the study, a total of n = 26 deaths were recorded from workers in U.S. nuclear power plants. Can the researcher use a z statistic for this hypothesis test? Explain your reasoning and/or show your work. d) (1 point) Out of the 26 recorded deaths, 10 of them were due to cancer. The researcher determined the p-value for this hypothesis test to be 0.0093. Based only on this p-value, is there significant evidence (should we reject Ho) to show that the proportion of deaths from cancer is greater for nuclear power plant workers? Explain your reasoning. PHST 301 Homework 6: 20 points Due: 11/20/23 11:59 PM 3) (5.5 points) A package of snack cakes claims that a single serving (one cake) has 160 calories. A consumer research group gathered a random sample of 40 cakes, which yielded a sample mean of 164 calories with a standard deviation of 18 calories. Is there evidence that the actual number of calories in these snack cakes is different from the 160 calories listed on the nutrition label? Test this hypothesis using a significance level of 5%. a) (0.5 points) What is the outcome variable? Is this outcome variable considered to be continuous or dichotomous? b) (1 point) Set up the appropriate null and alternative hypotheses for this study. c) (1 point) Select the appropriate test statistic. Should a z or t test statistic be used for this hypothesis test? Explain your reasoning and/or show your work. d) (0.5 points) Write out the decision rule for this hypothesis test. Make sure to include the appropriate z or t critical value. e) (1 point) Compute the appropriate test statistic for this hypothesis test. Show your work. f) (1 point) Make a decision using the decision rule in (d) and the calculated test statistic in (e). Write out an appropriate conclusion. g) (0.5 points) Do you expect the p-value for this test to be greater than or less than the significance level of 0.05? Explain. 4) (5.5 points) The extent to which an infant's health is affected by parental smoking is an important public health concern. The following data are the urinary concentrations of cotinine (a metabolite of nicotine); measurements were taken both from a sample of infants who had been exposed to household smoke (Group 1) and from a sample of unexposed infants (Group 2). The data are Sample size Sample mean Sample SD Exposed to household smoke 8 Unexposed 116.00 ng/mL 59.99 ng/mL 7 31.29 ng/mL 47.07 ng/mL Is there evidence that mean cotinine level for infants exposed to household smoke is greater than the mean cotinine level for unexposed infants? Test this hypothesis using a significance level of 1%. a) (0.5 points) What is the outcome variable? Is this outcome variable considered to be continuous or dichotomous? b) (1 point) Set up the appropriate null and alternative hypotheses for this study. c) (1 point) Select the appropriate test statistic. Should a z or t test statistic be used for this hypothesis test? Explain your reasoning and/or show your work. d) (0.5 points) Write out the decision rule for this hypothesis test. Make sure to include the appropriate z or t critical value. PHST 301 Homework 6: 20 points Due: 11/20/23 11:59 PM e) (1.5 points) Compute the appropriate test statistic for this hypothesis test. Show your work. f) (1 point) Make a decision using the decision rule in (d) and the calculated test statistic in (e). Write out an appropriate conclusion.