According to a recent Pew Research Center survey, 231 out of 371 Americans surveyed with just...

According to a recent Pew Research Center survey, 231 out of 371 Americans surveyed with just a high school diploma and 543 out of 634 Americans surveyed with a college degree have read at least one book in the last 12 months.

Based on these sample results and a 0.01 level of significance, can one infer that the proportion of Americans who have read at least one book in the last 12 months is higher for those with a college degree than for those with just a high school diploma?

Solutions

Expert Solution

Let , P1 be the population proportion of Americans surveyed with a college degree have read at least one book in the last 12 months and P2 be the population proportion of Americans surveyed with a school diploma have read at least one book in the last 12 months

Given : n1=634 ,X1=543 ,n2=371 , X2=231

The estimate of the sample proportions are ,

The pooled estimate is ,

Q=1-P=0.2299

Hypothesis: Vs

The critical value is ,

; From Z-table

The test statistic is ,

Decision : Here , teh value of the test statistic lies in the rejection region.

Therefore , reject Ho.

Conclusion : Hence , there is sufficien evidence to support the claim that the proportion of Americans who have read at least one book in the last 12 months is higher for those with a college degree than for those with just a high school diploma.

orchestra answered 1 year ago

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