Question

A report suggests that business majors spend the least amount of time on course work than...

A report suggests that business majors spend the least amount of time on course work than all other college students (The New York Times, November 17, 2011). A provost of a university decides to conduct a survey where students are asked if they study hard, defined as spending at least 20 hours per week on course work. Of 120 business majors included in the survey, 20 said that they studied hard, as compared to 48 out of 150 nonbusiness majors who said that they studied hard. (You may find it useful to reference the appropriate table: z table or t table)

Let p1 represent the population proportion of business majors who study hard, and p2 the population proportion of non-business majors who study hard.


a. State the hypotheses to test if proportion of business majors who study hard is less than that of the non-business majors.

  • H0: p1 − p2 ≤ 0; HA: p1 − p2 > 0

  • H0: p1 − p2 ≥ 0; HA: p1 − p2 < 0

  • H0: p1 − p2 = 0; HA: p1 − p2 ≠ 0

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

c. Find the p-value.

  • p-value < 0.01

  • 0.01 ≤ p-value < 0.025

  • 0.025 ≤ p-value < 0.05

  • 0.05 ≤ p-value < 0.10

  • p-value ≥ 0.10

d. State the conclusion about whether the business majors who study hard is less than that of the non-business majors at the 5% level.

  • Reject H0; there is enough evidence to support the claim that the proportion of business majors who study hard is less than that of the non-business majors.

  • Reject H0; there is not enough evidence to support the claim that the proportion of business majors who study hard is less than that of the non-business majors.

  • Do not reject H0; there is enough evidence to support the claim that the proportion of business majors who study hard is less than that of the non-business majors.

  • Do not reject H0; there is not enough evidence to support the claim that the proportion of business majors who study hard is less than that of the non-business majors.

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