Question

A college claims that 25% of its students receive tuition discounts. In a sample of 150 students, 35 of the students receive tuition discounts.

a. Using a significance level of α=0.1, perform a two-tailed hypothesis test to determine if the college’s claim is being met. Use the confidence interval approach.

b. Repeat part (a), but use the p-value approach.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.25

H_a : p 0.25

N = 150

X = 3

= x / n = 35 / 150 = 0.23

P₀ = 0.25

1 - P₀ = 1 -0.25 = 0.75

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.23 -0.25 / [0.25* 0.75 /150 ]

= −0.471

Test statistic = z = −0.47

a ) P-value = 0.6374

= 0.10

P-value ≥

0.6374  ≥ 0.10

b ) The null hypothesis Ho is not rejected.

Therefore, there is not enough evidence to claim that the population proportion p is different than P₀ at the \alpha = 0.10α=0.10 significance level