A Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer; a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer. Test whether there is a difference between these proportions at α = 0.05. What is the test statistic value? Group of answer choices

According to the question,

Women,

Men,

Now,

The pooled estimate of the proportion will be:

→

By substituting the values,

then,

→

hence,

The test statistics:

→

By putting the values, we get

Thus the above response is right.  

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Step-by-step explanation:

Step(i):-

Given first random sample size n₁ = 500

Given  Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer.

First sample proportion

Given second sample size n₂ = 700

Given a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer.

second sample proportion

Level of significance = α = 0.05

critical value = 1.96

Step(ii):-

Null hypothesis : H₀: There  is no significance difference between these proportions

Alternative Hypothesis :H₁: There  is significance difference between these proportions

Test statistic

where

       Q = 1 - P = 1 - 0.165 = 0.835

Z =  -2.76

|Z| = |-2.76| = 2.76 > 1.96 at 0.05 level of significance

Null hypothesis is rejected at 0.05 level of significance

Alternative hypothesis is accepted at 0.05 level of significance

Conclusion:-

There is there is a difference between these proportions at α = 0.05

b

step-by-step explanation:

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