Question

1. The Advisory Council for a college of business wants to know if the true proportion of graduates who use statistical inference within the first year after graduation is greater than 0.5. If so, the college plans to use this finding to propose that a new "data science" course be added to the list of courses offered in the college. A marketing research firm was hired to perform a study.

   After taking a sample of 750 recent graduates, the firm hired by the council found that 391 students indicated that they did use statistical inference within a year of graduation. Perform a hypothesis test at the 0.05 level of significance by filling in the blanks below. Type the correct symbols, words, and numbers. Type < for "less than," > for "greater than", = for "equal to", etc. as needed.

   1). Hypotheses

   H₀: p  ≤ (BLANK)

   H₁: p > 0.50

   2). Test Statistic.  Take all calculations to four (4) decimal places; enter your answer to two (2) decimal places.

   z = (BLANK)

   3). Rejection (or Critical) Region.

   All z > (BLANK)

   4). Conclusion (in the context of the problem). Enter one of the terms in parentheses for each blank in this section.

   The Advisory Council will  (reject/fail to reject) the null hypothesis. They  (can/cannot) conclude that the true proportion of graduates who use statistical inference is greater than 0.5.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: p <= 0.5
Alternative Hypothesis: p > 0.5

2)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.5213 - 0.5)/sqrt(0.5*(1-0.5)/750)
z = 1.17

3)

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

4)

The Advisory Council will (fail to reject) the null hypothesis. They (cannot) conclude that the true proportion of graduates who use statistical inference is greater than 0.5.