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In: Statistics and Probability

In a survey of 176 females who recently completed high​ school, 75​% were enrolled in college....

In a survey of 176 females who recently completed high​ school, 75​% were enrolled in college. In a survey of 180 males who recently completed high​ school, 65​% were enrolled in college. At alpha equals 0.09​, 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​ (b) through​ (e). ​(b) Find the critical​ value(s) and identify the rejection​ region(s). ​(c) Find the standardized test statistic. ​(d) Decide whether to reject or fail to reject the null hypothesis. ​(e) Interpret the decision in the context of the original claim.

Solutions

Expert Solution

Let , p1 be the population proportion of females and p2 be the population proportion of males.

Given : n1=176 , p1=0.75 , n2=180 , p2=0.65

The pooled estimate for proportion is ,

Q=1-P=0.3006

Claim : there is no difference in the proportion of college enrolled between the two​groups

Hypothesis : VS  

(b) Critical values are given by ,

; From normal probability integral table

Rejection region :

(c) The standardized test statistic is ,

(d) Here , the value of the test statistic is fall in the rejection region.

Therefore , reject Ho.

(e) Interpretation :

Hence , there is sufficient evidence to reject the claim that there is no difference in the proportion of college enrolled between the two​groups

orchestra answered 1 year ago
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