Mathematics, 16.06.2020 17:57 lauralimon

In a random sample of A women, 65% favored stricter gun control laws. In a random sample of B men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of C

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Answer from: ddea4081

We conclude that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control.

Step-by-step explanation:

The complete question is : In a random sample of 360 women, 65% favored stricter gun control laws. In a random sample of 220 men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of 0.05.

Now, we are given that in a random sample of 360 women, 65% favored stricter gun control laws.

And in a random sample of 220 men, 60% favored stricter gun control laws.

Let p_1 = proportion of women favoring stricter gun control laws.

p_2 = proportion of men favoring stricter gun control laws.

SO, Null Hypothesis, H_0 : $p_1\leq p_2$ {means that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control}

Alternate Hypothesis, H_A : p_1 p_2 {means that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control}

The test statistics that would be used here Two-sample z-test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of women favoring stricter gun control laws = 65%

$\hat p_2$ = sample proportion of men favoring stricter gun control laws = 60%

n_1 = sample of women = 360

n_2 = sample of men = 220

So, the test statistics = $\frac{(0.65 -0.60)-(0)}{\sqrt{\frac{0.65(1-0.65)}{360}+\frac{0.60(1-0.60)}{220} } }$

= 1.205

The value of z test statistics is 1.205.

Now, at 5% significance level, the z table gives critical value of 1.645 for right-tailed test.

Since, our test statistics is less than the critical value of z as 1.205 < 1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control.

Answer from: Quest

Idon’t actually know but have you asked google yet

Answer from: Quest

step-by-step explanation: s

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