Question #13 A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacteria. The table Full data set shows the results for the number of bacteria per cubic foot for both types of rooms. A normal Carpeted Uncarpeted probability plot and boxplot indicate that the data are approximately normally distributed with no 9.9 12.5 12 10.1 12.8 6.1 outliers. Do carpeted rooms have more bacteria than uncarpeted rooms at the a = 0.01 level of 8.8 9.5 14.2 5.9 12.6 3.7 significance? 14.6 13.4 4.3 10.4 Click the icon to view the Student t-distribution table. What are the null and alternative hypotheses? Ho: "carpet = Hno carpet versus H1: Hcarpet > Ino carpet Calculate the test statistic, to- to =(Round to two decimal places as needed.) Now find the critical value. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. to = B. to/ 2 =Question #15 A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. Two sample T for Men vs Women She randomly selected 56 men and 76 women to participate in the study. Each subject was required to step up and N Mean StDev SE Mean down a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained. Men 56 112.5 11.1 1.5 Women 76 118.6 14.6 1.7 90% CI for mu Men - mu Women (-9.83, -2.37) T-Test mu Men = mu Women (vs H2 (b) Identify the P-value and state the researcher's conclusion if the level of significance was o = 0.01. What is the P-value? P-value = (c) What is the 95% confidence interval for the mean difference in pulse rates of men versus women? The lower bound is The upper bound is (Round to two decimal places as needed.)Question #16 A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences and obtains the accompanying data. Complete parts (a) through (e). Click the icon to view the data table. (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. The least-squares regression line is y=|]x + . (Round to four decimal places as needed.) - X Data Table Full data set Head Head Height, X circumference, Height, x circumference, (inches) y (inches) (inches) y (inches) 27.75 17.7 26.5 17.3 24.5 17.1 27.5 17.5 25.5 17.1 26.75 17.3 25.5 17.3 26.75 17.5 25 16.9 27.5 17.5 27.75 17.6 (b) Use the regression equation to predict the head circumference of a child who is 25 inches tall. The predicted value of the head circumference of a child who is 25 inches tall is inches. (Round to two decimal places as needed.) (c) Compute the residual based on the observed head circumference of the 25-inch-tall child in the table. Is the head circumference of this child above average or below average? The residual based on the observed head circumference of the 25-inch-tall child is inches. (Round to two decimal places as needed.)