A study showed that 69% of supermarket shoppers believe supermarket brands to be

Question

A study showed that 69% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup.

a. Formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differed from 69%.

b. If a sample of 100 shoppers showed 52 stating that the supermarket brand was as good as the national brand, what is the p-value (to 4 decimals)?

_________

c. At = .05, what is your conclusion?

p-value is _______ H0

d. Should the national brand ketchup manufacturer be pleased with this conclusion?

YES OR NO?

Since p = _______ , it indicates that ____ (Fewer or Larger?) than _______ % of the shoppers believe the supermarket brand is as good as the name brand.

Select greater than or equal to 0.69 greater than 0.69 less than or equal to 0.69 less than 0.69 equal to 0.69 not equal to 0.69

Explanation / Answer

a)
Below are the null and alternate hypothesis
H0: p is equal to 0.69
H1: p is not equal to 0.69

b)
pcap = 52/100 = 0.52
SE = sqrt(0.69*0.31/100) = 0.04625

test statistics, z = (0.52 - 0.69)/0.04625= -3.6756

p-value = 0.000237

c)
p-value is less than 0.05, reject H0

d)
This is good for national brand ketchup manufacturer.
Since p = 0.000237, it indicates that fewer than 0.2% of the shoppers believe the supermarket brand is as good as the name brand

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