316 CHAPTER 6. INFERENCE FOR CATEGORICAL DATA 6.16 Is college worth it? Part I.

Question

316 CHAPTER 6. INFERENCE FOR CATEGORICAL DATA 6.16 Is college worth it? Part I. Among a simple random sample of 331 A decided not to go to college because they could not afford school.4 American said they (a) A newspaper article states that only a minority of the Americans who decide not ollege do so because they cannot afford it and uses the point estimate from this co evidence. Conduct a hypothesis test to determine if these data provide to go to as supporting this statement. strong evidence t a confidence interval for the proportion of American adults who decide not (b) Would you expec o to college because they cannot afford it to include 0.52

Explanation / Answer

R code :

> 0.48*331
[1] 158.88
> prop.test(159,331,alt="l")

1-sample proportions test with continuity correction

data: 159 out of 331, null probability 0.5
X-squared = 0.43505, df = 1, p-value = 0.2548
alternative hypothesis: true p is less than 0.5
95 percent confidence interval:
0.0000000 0.5270118
sample estimates:
p
0.4803625

a) Since p-value < 0.05, we reject the null hypothesis and conclude that the proportion of American adults deciding not to go to college is significantly less than 0.5 and hence there is strong evidence in support of the given statement.

b) Yes, the 95% confidence interval does contain 0.5.

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