Question

54% of students entering four-year colleges receive a degree within six years. Is this percent larger for students who play intramural sports? 453 of the 800 students who played intramural sports received a degree within six years. What can be concluded at the 0.1 level of significance?

H₀: p = 0.54

1. H_a: p __ 0.54: a. >

b. <

c. Not equal to

2. Test Statistic: a. 0.57

b. 0.07

c. 1.49

d. -1.43

3. Critical Value: a. 2.33

b. 1.645

c. 1.28

d. 1.96

4. p-value: (Round your number to three decimal places) a. 0.068

b. 1.49

c. 0.136

d. 0.034

5. Reject the null hypothesis or fail to reject null hypothesis?

6. Conclusion: a. sufficient evidence

  b. Insufficient evidence

Answer 1

1)

H0: p = 0.54

Ha: p > 0.54

2)

Sample proportion = 453 / 800 = 0.5663

Test statistics

z = - p / sqrt( p (1 -p) / n)

= 0.5663 - 0.54 / sqrt(0.54 * 0.46 / 800)

= 1.49

3)

At 0.1 significance level,

Critical value = 1.28

4)

p-value = P( Z > z) = P( Z > 1.49)

= 0.068

5)

Since p-value < 0.1 significance level, reject the null hypothesis.

6)

We conclude at 0.1 level that we have sufficient evidence to support the claim.