Question

1. A market research study is designed to determine if more than 25% of the residents of a large city would be a new type of cereal. A random sample of 600 people is selected and is given the new cereal to try. The 600 people are then asked if they would buy this cereal and 168 responded they would. At α = 0.05, is there enough evidence to conclude that more than 25% of the residents of this city would buy the new type of cereal? Use the p-value method.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.25

Ha : p > 0.25

= x / n = 168 / 600 = 0.28

P0 = 0.25

1 - P0 = 1-0.25 = 0.75

Test statistic = z

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

= 0.28 - 0.25 / [0.25*(0.75) / 600]

= 1.697

P(z >1.697 ) = 1 - P(z <1.697 ) = 0.0448

P-value = 0.0448

= 0.05    

0.0448 < 0.05

Reject the null hypothesis .

There is enough evidence to claim that the population proportion p is greater than 25%, at the α=0.05 significance level.