Question

3. In a recent survey of gun control laws, a random sample of 1000 women showed that 65% were in favor of stricter gun control laws.  In a random sample of 1000 men, 60% favored stricter gun control laws.  Test the claim that the percentage of men and women favoring stricter gun control laws is the same at α=0.05

1 H₀:_________   H_a:____________                       5.Decision:{Circle one}Reject H₀ or Fail to Reject H₀

2 α=_________                                                   6. P-value ____________

3 Critical Value   _________                                 7.Statement:___________________________________

                                                                                          ___________________________________

4Test stat___________                                                                 

Answer 1

Here in this scenario it is given that the survey of gun control laws, a random sample of 1000 women showed that 65% were in favor of stricter gun control laws that means out of 1000 650 womens are in favour of sticker gun control law.

And In a random sample of 1000 men, 60% favored stricter gun control laws that means 600 men are in favour of gun control law .

Our claim is that the percentage of men and women favoring stricter gun control laws is not same.

To test this claim we have to use two sample proportion z test.

The z test for two population proportion is performed at 0.05 level of significance as below,

The z critical value is calculated using Standerd normal z-table or using Excel. At two tailed 0.025 level of significance.

1 H₀:P1 = P2 H_a: P1=×= P2   

  5.Decision:

Reject H_0.

Since p value is less than Alpha level of significance so we Reject Ho null hypothesis at 0.05 level of significance.

2 α= 0.05

6. P-value = 0.0209

The p value is calculated using Standerd normal z-table.

3 Critical Value -1.96 & 1.96.

The value of Test stat Z cal = 2.309.

Since p value is less than alpha 0.05 level of significance so we Reject Ho null hypothesis and concluded that the proportion or percentage of men and women are not same at 0.05 level of significance.

Thank you.