STA 261 Due- Jeu . C Homework # 13 Suppose Ford is planning to produce two new t

Question

STA 261 Due- Jeu . C Homework # 13 Suppose Ford is planning to produce two new types o f SUVs, the "Grand Canyon" and the rest." They want to know the fuel efficiency of these two new SUVs, so they test 26 Grand Canyons Canyon is 11.1 the Evere and 22 Everests. They find that the mean fuel efficiency for the Grand mpg with a standard deviation of 2.77 mpg, and the mean fuel efficiency of st is 12.2 mpg with a standard deviation of 3.44 mpg. Find a 95% confidence interval for the difference in the mean gas mileage of the two SUVs and explain what your interval means. a)

Explanation / Answer

Q.1 (a) Here the data set is

Here pooled standard deviation sp = sqrt [(n1 -1)s12 + (n2 -1)s22 } /(n1 + n2 -2)] = sqrt [(25 * 2.772 + 21 *3.442 )/(25+21)] = 3.094

HEre standard error of difference in means = sp  * sqrt(1/n1 + 1/n2 ) = 3.094 * sqrt (1/26 + 1/22) = 0.8963

so

95% confidence interval for difference = (x2-x1 ) +- t46,0.05 se0

= (12.2 - 11.1) +- 2.0129 * 0.8963

= (-0.704, 2.904)

(b) H0 : 1 = 2

Ha : 1 2

Test statistic

t = (x2-x1 )/ se0 = (12.2 - 11.1)/ 0.8963 = -1.2273

critical value for alpha = 0.05, dF = 46

t46,0.05 = 2.0129

so here l t l < tcritical so we fail to reject the null hypothesis and can conclude that the mean gas mileage is same for both the cars.

Grand Canyon Everest n 26 22 Mean(xi) 11.1 12.2 Std.dev.(si) 2.77 3.44

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