Question

1. In a random sample of 200 college graduates, 42 said that they think a college degree is not worth the cost. Test to see if this sample provides significant evidence that the population proportion of college graduates who believe a college degree is not worth the cost is DIFFERENT FROM 25%. Use a 5% significance level. Round all calculations to three decimal places. Verify that the sample size is large enough (2 short calculations)

a. Write the null and alternate hypothesis

b. Calculate the observed sample statistic Calculate z score

c. Find p-value for the test

d. Formal decision: Reject Ho or Do Not Reject Ho

e. Write a sentence explaining the conclusion of the text in context.

Answer 1

Q.1) Given that, n = 200 and x = 42

=> sample proportion = 42/200 = 0.21

We want to test to see if this sample provides significant evidence that the population proportion of college graduates who believe a college degree is not worth the cost is DIFFERENT FROM 25%.

Sample size is large enough, because, np0 = 200 * 0.25 = 50 and

n(1-p0) = 200 * (1-0.25) = 200 * 0.75 = 150 and both are greater than 10.

a) The null and alternative hypotheses are,

Null Hypothesis : H0 : p = 0.25

Alternative Hypothesis : Ha : p ≠ 0.25

b) Test statistic is,

The observed sample statistic = Z = -1.306

c) p-value = 2 * P(Z < -1.306) = 2 * NORMSDIST (-1.306) = 0.1915

=> p-value = 0.191

d) Since, p-value is greater than significance level of 0.05, we do not reject H0.

e) Conclusion : There is not sufficient evidence to conclude that the population proportion of college graduates who believe a college degree is not worth the cost is DIFFERENT FROM 25%.