Question

In 2009, the Southeastern Conference (SEC) commissioner set a goal to have greater than 65% of athletes that are entering freshmen graduate in 6 years. In 2015, a sample of 100 entering freshmen from 2009 was taken and it was found that 70 had graduated in 6 years. Does this data provide evidence that the commissioner’s graduation goal was met (α = .10)?

The value of the test statistic is ________ and the critical value is _________.

1.05; -1.282
		+1.05; +1.282
		-1.27; ±2.576
		-1.73; ±1.645

Answer 1

Solution :

Given that,

= 0.65

1 - = 0.35

n = 100

x = 70

Level of significance = = 0.10

Point estimate = sample proportion = = x / n = 0.7

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.65

Ha: p 0.65

Test statistics

z = ( - ) / *(1-) / n

= ( 0.7 - 0.65) / (0.65*0.35) /70

= 1.05

Critical value of  the significance level is α = 0.10, and the critical value for a right-tailed test is

= 1.282

The answer is ( +1.05 , + 1.282 )