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Chapter 9: Q 38. (page 581)

Fire the coach!A college president says, “More than two-thirds of the alumni support my firing of Coach Boggs.” The president’s statement is based on 200emails he has received from alumni in the past three months. The college’s athletic director wants to perform a test of H0:p=2/3versus Ha:p>2/3, where p= the true proportion of the college’s alumni who favor firing the coach. Check if the conditions for performing the significance test are met.

Short Answer

Expert verified

All conditions are fulfilled.

Step by step solution

01

Given Information

It is given that n=200

p=23

The null and alternate hypothesis are:

H0:p=23

Ha:p>23

02

Calculation

The conditions important for significance test are:

  • n×p≥10: role="math" localid="1654611425980" n×p=200×23=133.333>10
  • n×(1-p)≥10: n×(1-p)=200×1-23=66.667>10

All condition are fulfilled, significance test can be performed.

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Most popular questions from this chapter

AttitudesThe Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' attitudes toward school and study habits. Scores range from 0 to 200 . Higher scores indicate better attitudes and study habits. The mean score for U.S. college students is about 115. A teacher suspects that older students have better attitudes toward school, on average. She gives the SSHA to an SRS of 45 of the over 1000 students at her college who are at least 30 years of age.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

Losing weight A Gallup poll found that 59% of the people in its sample said “Yes” when asked, “Would you like to lose weight?” Gallup announced: “For results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is ±3 ±3percentage points.”12 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they want to lose weight differs from 0.55? Explain your reasoning

In a test ofH0:p=0.4against Ha:p≠0.4, a random sample of size 100 yields a standardized test statistic of z=1.28. Which of the following is closest to the P-value for this test?

a. 0.90

b. 0.40

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d. 0.20

e. 0.10

No homework? Mr. Tabor believes that less than 75%of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of 50 students at the school.

Powerful potatoes Refer to Exercise 85. Determine if each of the following

changes would increase or decrease the power of the test. Explain your answers.

a. Change the significance level to α=0.10

b. Take a random sample of 250 potatoes instead of 500 potatoes.

c. The true proportion is p=0.10 instead of p=0.11
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