Question

A dean of a business school wants to know if the proportion of graduates who use statistical inference within the first year after graduation is greater than 0.6. Suppose the test statistic was found to be 1.01. At the a = 0.10 level of significance, what would be the conclusion?

Answer using only the information presented in this question; do not refer to your answers to any other questions that might have a similar set-up.

Read carefully, and select all that apply!

a) Conclude that the true proportion of graduates who use statistical inference one year after graduation is greater than 0.60. That is, more than 60% of graduates use statistical inference one year after graduation.

b) Conclude that the true mean number of graduates who use statistical inference one year after graduation is greater than 60/300 = 0.20. That is, more than 20% of graduates use statistical inference one year after graduation.

c) Conclude that the true proportion of graduates who use statistical inference one year after graduation is greater than 0.10. That is, more than 10% of graduates use statistical inference one year after graduation.

d) Fail to reject the null hypothesis

e) Reject the null hypothesis.

f) Conclude that the true mean number of graduates who use statistical inference one year after graduation is greater than 0.60. That is, an average of 60 graduates use statistical inference one year after graduation.

g) Reject the alternative hypothesis

h) Cannot conclude that the true mean number of graduates who use statistical inference one year after graduation is greater than 0.60. That is, the Dean cannot claim that an average of more than 60 graduates use statistical inference one year after graduation.

i)	Cannot conclude that the true proportion of graduates who use statistical inference one year after graduation is greater than 0.60. That is, the Dean cannot claim that more than 60% of graduates use statistical inference one year after graduation.

Answer 1

P-value = P(Z > 1.01)

= 1 - P(Z < 1.01)

= 1 - 0.8438

= 0.1562

At alpha = 0.10, since the P-value is greater than the significance level (0.1562 > 0.10), we should not reject the null hypothesis .

Option-d) Fail to reject the null hypothesis.

Option - e) Reject the alternative hypothesis .

i) Cannot conclude that the true proportion of graduates who use statistical inference one year after graduation is greater than 0.60. That is, the Dean cannot claim that more than 60% of graduates use statistical inference one year after graduation.