Question

Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 41 women athletes at the school showed that 23 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 1% level of significance.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.67

H_a : p < 0.67

n = 41

x = 23

= x / n = 23 / 41 = 0.561

P₀ = 0.67

1 - P₀ = 1 - 0.67 = 0.33

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.561 - 0.67 / [(0.67 * 0.33) / 41]

= -1.485

Test statistic = -1.49

P(z < -1.485) = 0.0688

P-value = 0.0688