Question

Jamie is doing a survey at her school about whether the students feel the cafeteria food is satisfactory. She records the responses of 120 students and finds that 40% find the food satisfactory. She wonders whether she can claim this is significantly less than half with significance 0.1.

Step 5 of 6: State your conclusion and rationale.

Step 6 of 6: Interpret your previous answer.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p < 0.5

n = 120

= 0.40

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.40 - 0.5 / [(0.5 * 0.5) / 120]

= -2.19

Test statistic = -2.19

P(z < -2.19) = 0.0143

P-value = 0.0143

= 0.1

P-value <

Reject the null hypothesis .

There is sufficient evidence that she can claim this is significantly less than half with significance 0.1 .