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Math  /  Data & Statistics

QuestionIn a survey of 200 females who recently completed high school, 76%76 \% were enrolled in college. In a survey of 150 males who recently completed high school, 68%68 \% were enrolled in college. At α=0.07\alpha=0.07, can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e). (a) Identify the claim and state H0\mathrm{H}_{0} and Ha\mathrm{H}_{\mathrm{a}}.
The claim is "the proportion of female college enrollees is □\square the proportion of male college enrollees."

Studdy Solution

STEP 1

1. We have two independent samples: 200 females and 150 males.
2. The proportion of females enrolled in college is 76%76\%.
3. The proportion of males enrolled in college is 68%68\%.
4. We are testing the claim that there is no difference in the proportion of college enrollees between the two groups.
5. The significance level is α=0.07\alpha = 0.07.

STEP 2

1. Identify the claim and state the null and alternative hypotheses.

STEP 3

Identify the claim: The claim is "the proportion of female college enrollees is equal to the proportion of male college enrollees."

STEP 4

State the null hypothesis (H0\mathrm{H}_{0}): H0:p1=p2\mathrm{H}_{0}: p_1 = p_2 Where p1p_1 is the proportion of female college enrollees and p2p_2 is the proportion of male college enrollees.

STEP 5

State the alternative hypothesis (Ha\mathrm{H}_{a}): Ha:p1≠p2\mathrm{H}_{a}: p_1 \neq p_2
The claim is "the proportion of female college enrollees is equal to the proportion of male college enrollees."
The null hypothesis is H0:p1=p2\mathrm{H}_{0}: p_1 = p_2.
The alternative hypothesis is Ha:p1≠p2\mathrm{H}_{a}: p_1 \neq p_2.

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