complet 8.6 and then use 8.6 formula and complete 8.7 using excel

Using Excel a. Open the Prime data file. Note that the observations for the Expenditures variable are in cells B2 through B101. b. We use Excel's T.INV to find a particular to value. We enter =T . INV( cumulprob, of), where cumulprob is the cumulative probability associated with to and df is the degrees of freedom. For the 95% confidence interval with n = 100, we find to.025.99 using =T. INV(0. 975,99). Thus, in order to obtain the lower limit, we enter =AVERAGE(B2: B101) - T. INV (0. 975, 99) *STDEV . S(B2: 101) /SQRT (100). For the upper limit, we enter =AVERAGE (B2 : B101 ) + T. INV (0 . 975, 99) *STDEV . S(B2:101) /SQRT (100). Note: For a one-step approach to constructing a confidence interval in Excel, we can use the Descriptive Statistics option in its Analysis Toolpak which we discussed in L' Chapter 3. In the Descriptive Statistics dialog box, we select Summary statistics and Confidence Interval for Mean. (By default, the confidence level is set at 95%, but you easily enter another level.) In the table that Excel returns, we find the mean and the margin of error which is labeled Confidence Level(95.0%).EXAMPLE 8.7 In the introductory case of this chapter, Jared Beane wants to estimate the proportion of all ultra-green cars that obtain over 100 mpg. The MPG data file lists the mpg for a sample of 25 cars. Use the information to construct the 90% and the 99% confidence intervals for the population proportion. SOLUTION: In the MPG data file, we find that 25 cars obtain over 100 mpg; thus, the point estimate of the population proportion is p = 7/25 = 0.28. Note that the normality condition is satisfied, because np 2 5 and n(1 -p)2 5, where p is evaluated at p = 0.28. With the 90% confidence level, a/2 = 0.10/2 = 0.05; thus, we find za/2 = Zo.05 - 1.645. Substituting the appropriate values into p (1 - p) p+ Zo/2 1 yields n 0.28 + 1.6451 0.28 (1 - 0.28) = 0.28 + 0.148. 25 With 90% confidence, Jared reports that the percentage of cars that obtain over 100 mpg is between 13.2% and 42.8%. For the 99% confidence level, we use a/2 = 0.01/2 = 0.005 and za/2 = 20.005 = 2.576 to obtain 0.28 + 2.5761 0.28 (1 - 0.28) = 0.28 + 0.231. 25 At a higher confidence level of 99%, the interval for the percentage of cars that obtain over 100 MPG becomes 4.9% to 51.1%. Given the current sample size of 25 cars, Jared can gain confidence (from 90% to 99%) at the expense of precision, as the corresponding margin of error increases from 0.148 to 0.231