Question

1. The Pew Research Center reported in 2014 that Millennials with Bachelor’s degrees working full time are earning on average $17,500 more than those Millennials with only a high school degree ($45,500 vs. $28,000). Suppose in a random sample of 36 Millennials with Bachelor’s degrees taken today, the mean income was $50,000 with a sample standard deviation of $18,000. Test whether the population mean income of Millennials with Bachelor’s degrees has increased from the 2014 value of $45,500 at a significance level of α= 0.05.
   1. State the claim and the null and alternate hypotheses. Is the test left-, right-, or two-tailed?

2. Find the p-value of getting the sample data by chance. Show all work for credit (calculator inputs acceptable).

3. Decision: Reject H₀ or fail to reject H₀?

4. Conclude the result of the test in the context of the situation and in a statement that is understandable to a non-statistician.

Answer 1

a. The hypotheses are:

It is Right tailed test since the sample size is 36>30 hence we use Z statistic here

b) rejection region:

Reject Ho if Z >Z_0.05=1.65

Test statistic:

P-value:

P-value associated with Z score is computed using table shown below as 0.0474

c) Decision:

Since Z >Z_0.05 Hence we reject the null hypothesis.

d) Conclusion:

Since Z>Z_0.05 and P-value<0.05 hence reject the null hypothesis and conclude that there is sufficient evidence to support the claim that income has increased $ 45000.