Use a t-distribution to find a confidence interval for the difference in means µa = H1 – H2 using the relevant sample results from paired data. Assume the results come from random samples from populations that are approximately normally distributed, and that differences are computed using d = x1 – x2. A 99% confidence interval for u a using the paired data in the following table: Case 1 2 3 4 Treatment 21 28 30 26 28 1 Treatment 17 29 26 20 20 2 Give the best estimate for ua, the margin of error, and the confidence interval. Enter the exact answer for the best estimate, and round your answers for the margin of error and the confidence interval to two decimal places. best estimate = i margin of error = i The 99% confidence interval is i to i

a. What are the sample estimates of β0​,β1​,and β2​? b. What is the least squares prediction​ equation? c. FindSSE​,MSE​,and standard deviation . Interpret the standard deviation in the context of the problem. d. Test H0: β1=0 against Ha: β1≠0.Use α=0.01. e. Use a 95​% confidence interval to estimate β2. f. Find R2 and R^2_a and interpret these values. g. Find the test statistic for testing H0: β1=β2=0. h. Find the observed significance level of the test in part g.interpret the result.

Construct a 90% confidence interval for u, - , with the sample statistics for mean calorie content of two bakeries specialty pies and confidence interval construction formula below Assume the populations are approximately normal with equal variances Bakery A Bakery B X1 = 1823 cal X, = 1629 cal S1 = 155 cal S2 = 190 cal n1 = 10 n2 = 12 Confidence interval when variances are equal n n. (n. - 1) s (n2 - 1) s where G and d.f = n, +n2 - 2 nn, - 2 Enter the endpoints of the interval (Round to the nearest integer as needed.)

The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of fifteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. The least-squares regression line for these data has equation y = 40.86-0.45x. This line is shown in the scatter plot below. Mileage, x (in thousands) 29.7 27.8 26.8 24.2 21.1 23.0 24.3 15.4 37.7 23.6 34.4 27.8 23.5 20.9 259 Used selling price, y (in thousands of dollars) 27.4 29.4 31.2 30.1 31.7 31.7 27.2 34.2 23.4 28.2 26.3 26.5 33.7 30.6 267 Used selling price (in thousands of dollars) 40- 35+ 30- 25- 20 THIS 15 X 20 X X X 30 Mileagex (in thousands) X 35 40