Question

A study by consumer reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national brands. A manager of a local store believes that the percentage is higher in his store. She asks a random sample of 145 shoppers whether they believe that supermarket brand ketchup was as good as the national brand ketchup. Out of the 145 shoppers asked. 89 believed the supermarket brand was as good as the national brand. Use a 0.05 significance level and conduct a hypothesis test.  

Answer 1

Step 1:

Ho: p = 0.64

ha: p > 0.64

Null hypotheiss states that the proportion of supermarket shoppers believing supermarket brands to be as good as national brands is 0.64

ALternative hypotheiss states that the proportion of supermarket shoppers believing supermarket brands to be as good as national brands is greater than 0.64

Step 2: test statistics

n = 145

x =89

= x/ n = 89/145 = 0.6138

z = - 0.657

Step 3

level of significance = 0.05

z critical for right tailed test = 1.65

As z stat does not fall in the rejection area, we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that  the proportion of supermarket shoppers believing supermarket brands to be as good as national brands is greater than 0.64