Question

Jamie is doing a survey at her school about whether the students feel the cafeteria food is satisfactory. She records the responses of 160 students and finds that 45% find the food satisfactory. She wonders whether she can claim this is significantly less than half with significance 0.1.

A)What type of hypothesis test should be performed here?

B) State the null hypothesis and the alternative hypothesis.

C)Perform the appropriate test and state your p-value rounded to 4 decimal place.

D)State your conclusion and your rationale.

E)Interpret your previous answer.

Answer 1

Solution :

One sample proportion Z test

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p < 0.5

n = 160

= 0.45

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.45 - 0.5 / [(0.5 * 0.5) / 160]

= -1.265

Test statistic = -1.265

P(z < -1.265) = 0.1029

P-value = 0.1029

= 0.1

P-value >

Fail to reject  the null hypothesis .

There is not sufficient evidence to suggest that the claim is significantly less than half with significance 0.1 .