Question

Please label and show each step.

3. A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To understand whether this is applies to its own product; the manufacturer of a national name-brand cheese asked a sample of shoppers whether they believed that store brand cheese was as good as the name-brand cheese.

Consider the following hypothesis test:

H_o: π = 0.64

H₁: π ≠ 0.64

1. If a sample of 200 shoppers showed 110 stating that the supermarket brand was as good as the national brand, what would the computed value for the statistic be?

2. What is the p-value?

3. At a 0.05 level of significance, what would your decision be (reject Ho or fail to reject Ho)?

4. Would you consider the name-brand cheese to be any different in preference to the supermarket brand?

Answer 1

a.

Standard error of sampling distribution of proportions, SE = $\sqrt{p(1-p)/n} = \sqrt{0.64(1-0.64)/200} = 0.03394$

Observed proportion, p = 110 / 200 = 0.55

Test statistic, z = (Observed proportion - Hypothesized Proportion) / SE

= (0.55 - 0.64) / 0.03394

= -2.65

b.

P(z < -2.65) = 0.004

For two-tail test, p-value = 2 * 0.004 = 0.008

c.

As, p-value is less than the 0.05 level of significance, we reject H0.

d.

As, we reject H0, we conclude that there is significant evidence that $\pi \ne$ 0.64 or, there is significant evidence that the name-brand cheese is different in preference to the supermarket brand.