Question

A taste test was conducted between cheese steaks drawn from two competing restaurants: store A and store B. From previous records, the proportion of patrons within the city who preferred cheese steaks from store A was p = 0.5 . A staff member from the chamber of commerce is interested in knowing if those who prefer cheese steaks from store A has decreased. A random sample of 44 consumers were given small portions from each restaurant, with the same basic ingredients in each portion. From this sample, 18 consumers preferred cheese steaks from Store A. A level of α = .10 is chosen as the level of significance for the hypothesis test. From the test statistic z0 found in the question above, and consulting table V, the p-value is (choose the best answer): Group of answer choices .1635 .0559 .0985 .1131

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p < 0.50

n = 44

x = 18

= x / n = 18 / 44 =0.41

P0 = 0.50

1 - P0 = 1 - 0.50 = 0.50

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.41 -0.50 / [(0.50*0.50 ) / 44 )

= -1.21

Test statistic = z = -1.21

P(z <-1.21 ) = 0.1131

P-value = 0.1131

= 0.10

P-value <

0.1131 > 0.10

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that