<p>A sociologist suspects that women in the U.S. are \"marrying later in life\'

Question

<p>A sociologist suspects that women in the U.S. are "marrying later in life' today compared to in 1990 when the mean age of brides marrying for the first time was 20.8 years. In a recent sample of 36 women marrying for the first time the mean age awas 23.9 years with a standard deviation of 6.4 years. Using this data the sociologist wishes to determine if there is sufficient evidence that the mean age at which women marry for the first time today is higher than what it was in 1990. She uses &#945; = 0.05.</p>
<p>a. State the null and alternative hypotheses.</p>
<p>b. Find the critical value(s) and sketch the rejection region.</p>
<p>c. Find the test statistic.</p>
<p>d. Circle one: Reject H_o or Do not Reject H_o</p>
<p>e. State the conclusion in terms of the described study.</p>

Explanation / Answer

a. State the null and alternative hypotheses.

Ho: <=20.8
Ha: >20.8

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b. Find the critical value(s) and sketch the rejection region.

Given a=0.05, the critical value is Z(0.05)=1.645 (check standard normal table)

If Z>1.645, reject Ho.

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c. Find the test statistic.

Z=(23.9-20.8)/(6.4/6)

= 2.91

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d. Circle one: Reject H or Do not Reject H

Since Z= 2.91 > 1.645, we reject Ho.

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e. State the conclusion in terms of the described study.

So we can conclude that there is sufficient evidence that the mean age at which women marry for the first time today is higher than what it was in 1990

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