Question

The women athletes in the BIG10 Schools have a long-term graduation rate of 73%. Over the past several years, a random sample of 23 women showed that 19 graduated. Does this indicate that the population proportion of women athletes who graduate from the BIG10 is now more than 73%

Answer 1

This means that population proportion of women athletes who graduate from the BIG10 is now not more than 73%

Explanation:

Here,

The null hypothesis is p = 0.73

Alternate hypothesis is p> 0.73

The level of significance = 0.10 or 10%

Sample size = 23

Sample proportion = 19/23 = 0.826

Z test statistics

= (p’-p)/Sqrt ((p(1-p)/n))

Substituting the given values, we get –

Z = (0.826-0.73)/Sqrt ((0.73(1-0.73)/23)) = 1.037

Thus, the P values for Z>1.037

= 1- P(Z less than or equal to 1.037)

= 1- 0.8501

= 0.150

P-value is greater than the level of significance

We will accept the null hypothesis

This means that population proportion of women athletes who graduate from the BIG10 is now not more than 73%