Question

California Department of Education deems a student to be prepared for college if she scores higher than a certain score on the SAT. A survey was conducted looking at 538 students' SAT scores and it was found that 237 students were considered to be prepared for college. Use a 0.10 significance level to test the claim that the proportion of students prepared for college is at most 40%.
The test statistic is:    (to 2 decimals)

The p-value is:    ( 4 decimal places)

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.40

H_a : p <0.40

n = 538

x = 237

= x / n = 237 / 538 =0.44

P₀ = 0.40

1 - P₀ = 1 - 0.40 = 0.60

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.44 - 0.40/ [(0.40*0.60) / 538]

= 1.92

Test statistic = z = 1.92

P(z < 1.92 ) = 0.9726

P-value = 0.9726

= 0.10

P-value >

0.9726 > 0.10

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that