Question

Carry out (show all steps) the test to answer each of these questions. You may use either the classical method or the P -value method, but you must state the P -value for each problem.

1. A simple random sample of 320 adults was asked their favorite ice cream flavor. Of the 320 individuals surveyed, 58 responded that they preferred mint chocolate chip. Test the claim that less than 25% of adults prefer mint chocolate chip ice cream at the α = 0.05 level of significance.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.25

H_a : p < 0.25

n = 320

x = 58

= x / n = 58 / 320 =0.18

P₀ = 0.25

1 - P₀ = 1 - 0.25 = 0.75

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.18 - 0.25/ [(0.25*0.75) / 320]

= -2.84

Test statistic = z = -2.84

P(z < -2.84 ) = 0.0023

P-value = 0.0023

= 0.05

P-value <

0.0023 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that