Question

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 LaTeX: \alpha α = 0.01, the conclusion for this hypothesis test would be that because the test statistic is _______________________________________________________________. less than 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 less than 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 more than 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 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 none of these answers are correct

Answer 1

Given that, n1 = 200 , x1 = 126 and n2 = 175, x2 =119

significance level of α = 0.01

The null and the alternative hypotheses are,

H₀ : p₁ = p₂

H₁ : p₁ < p₂

Using TI-84 calculator we get,

Test statistic is, Z = -1.01

since it is left-tailed test, critical value at α = 0.01 is, -2.33

Therefore, the conclusion for this hypothesis test would be that because the test statistic is (-1.01) more than the critical value ( -2.33 ), 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.