Question

Question 9 1.25 pts AT&T would like to test the hypothesis that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans. A random sample of 200 18- to 34-year-old Americans found that 126 owned a smartphone. A random sample of 175 35- to 49-year-old Americans found that 119 owned a smartphone. If Population 1 is defined as 18- to 34- year-old Americans and Population 2 is defined as 35- to 49-year-old Americans, and using a = 0.01, the conclusion for this hypothesis test would be that because the absolute value of the test statistic is less than the absolute value of the critical value, AT&T can conclude that the proportion of 18- to 34-year-old Americans that own a cell phone less than the proportion of 35- to 49-year-old Americans less than the absolute value of the critical value, AT&T cannot conclude that the proportion of 18- to 34-year- old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans O more than the absolute value of the critical value, AT&T can conclude that the proportion of 18-to 34-year- old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans more than the absolute value of the critical value, AT&T cannot conclude that the proportion of 18-to 34- year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans

Answer 1

Given :

X1 = 126, n1 = 200

X2 = 119, n2 = 175

Sample proportion = ${\hat{p}}$ = X/n

${\hat{p}}$1 = X1/n1 = 126/200 = 0.63

${\hat{p}}$2 = X2/n2 = 119/175 = 0.68

Pooled proportion :

${\bar{p}}$ = X1+X2/n1+n2 = 126+119/200+175 = 0.6533

Hypothesis test :

The null and alternative hypothesis is

Ho : p1 = p2

Ha : p1 < p2

Test statistic :

0.63 -0.68 z= -² PC1-) Chitra) 0.6533(1-0.6533 3) € 200 +175) = -1.01 Z-[-1.0) Critical value fora=0.01 7212= 20.01/2 = -2.33 Dicision Rule :- Reject Ho, if z<-2.33. Since z}-2.33, we fail to reject Ho,

Since test statistic is more than the absolute value of the critical value, AT&T cannot conclude that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.

Answer - option D