A study showed that 65% of supermarket shoppers believe supermarket brands to be

Question

A study showed that 65% 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 65%.

H0: p is ____
Ha: p is ____

b. If a sample of 100 shoppers showed 51 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 0.65 greater than 0.65 less than or equal to 0.65 less than 0.65 equal to 0.65 not equal to 0.65

Explanation / Answer

as we are saying as good as then it means that it could be greater than equal to national average

so

H0: less than 0.65

Ha : greater than or equal to 0.65

here p = 0.65

and phat = 51/100 = 0.51

so we use the formula as

z = (phat - p)/sqrt(p*(1-p)/n)

= (0.51 - 0.65)/sqrt(0.65*(1-0.65)/100)
= -2.935

we check the p value from the z table as
P ( Z>2.935 )=P ( Z<2.935 )=0.9984

as the p value is not less than 0.05 , hence we fail to reject the null hypothesis

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