In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men, 60% favored increasing the legal drinking age. Test the claim that the percentage of men and women favoring a higher legal drinking age is different at (alpha 0.05).

Step-by-step explanation:

Given that:

Let sample size of women be  = 1000

Let the proportion of the women be = 0.65

Let the sample size of the men be = 1000

Let the proportion of the mem be  = 0.60

The null and the alternative hypothesis can be computed as follows:

Thus from the alternative hypothesis we can realize that this is a two tailed test.

However, the pooled sample proportion p =

p =

p =

p = 0.625

The standard error of the test can be computed as follows:

The test statistics is :

At level of significance of 0.05  the critical value for the z test will  be in the region between - 1.96 and 1.96

Rejection region: To reject the null hypothesis if z < -1.96 or z > 1.96

Conclusion: Since the value of z is greater than 1.96, it lies in the region region. Therefore we reject the null hypothesis and we conclude that  the percentage of men and women favoring a higher legal drinking age is different.

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