Problem 12 Red Blood Cells: Drug Effects [10 points] calculator A medical research team (Journal of Hematology & Oncology) is studying the effect of a new drug on red blood cells. Let x be a random variable representing milligrams of the drug given to a patient. Let y be a random variable representing red blood cells per cubic milliliter of whole blood. A random sample of n = 7 volunteer patients gave the following results. coefficients and answers to three decimal places X 9.2 10.1 9.0 12.5 8.8 9.1 9.5 5.0 4.8 4.5 5.7 5.1 4.6 4.2 (a) What is the correlation coefficient for this data set? Interpret this value in relation to this problem. (b) Run a linear correlation hypothesis test to determine whether there is significant linear correlation between the drug and red blood cells. Use a = 0.05. State your conclusion. Ho: Ha: Calculator Function Used: test statistic value: p-value: (c) What is the equation for the least-squares line? coefficients to three decimal places (d) Compute the coefficient of determination. Interpret this value in relation to this problem. (e) If the variable x = 11.02, what does the least-squares line predict for y.? (f) A current test sample has an x = 4.9. Would you use this model to predict y? Why or why not?Problem 13 Census: Type of Household [6 points] calculator The type of household for the U.S. population and for a random sample of 411 households from the community of Dove Creek, Montana, are shown below (based on Statistical Abstract of the United States). Use a 1% level of signicance to test the claim that the distribution of US. households ts the Dove Creek distribution. show your work Observed Number of cheeholcle In \" Married. no children 29% 112 all-tote parent One person Other (e.g.. roommates. elhllngc) Calculator Function: v: test statistic value: p-value: Conclusion in terms of this problem. Problem 14 Medical: Headache Remedies [2 points] Two competing headache remedies claim to give fast- acting relief. An experiment was performed to compare the mean time required for bodily absorption of brand A and brand B headache remedies. Twelve subjects were given an oral dosage of brand A while 15 subjects were given an equal dosage of brand B. Are these independent or dependent samples? circle your answer independent dependent need more information Problem [5 Medical: REM Sleep [7 points] calculator REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults (Reference: Secrets ofSieep by Dr. A. Borbely). Assume that REM sleep time is normally distributed for both children and adults. A random sample of He: 10 children showed that they had an average REM sleep time of it, = 2.8 hours per night. From previous studies, it is known that cl = 0.5 hour. Another random sample of m= 10 adults showed that they had an average REM sleep time of in = 2.1 hours per night. Previous studies show that o. = 0.7 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? (8) Perform the appropriate hypothesis test to determine the e'ectiveness of Borbely's claim. Use ct = 0.05. Ho: Ha: Calculator Function Used: test statistic value: p-value: Conclusion: (b) Construct the condence interval to conform to the hypothesis test conducted in part (a). What conclusion does the condence interval suggest? Calculator Function Used: Confidence Interval: Conclusion and interpretation in terms oi'this