A study showed that 61% of supermarket shoppers believe supermarket brands to be
ID: 3316508 • Letter: A
Question
A study showed that 61% 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 61%. 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? . Since p = , it indicates that than % of the shoppers believe the supermarket brand is as good as the name brand.
Explanation / Answer
Solution:
a. Null hypothesis H0: p = 0.61.
Alternative hypothesis Ha: p 0.61.
b. Check
np0 = 100 * 0.61 = 61 > 5
n(1 p0) = 100 * (1 0.61) = 100 * 0.39 = 39 > 5
Test statistic: Z = 0.510.61/sqrt(0.61039/100) = -2.05.
Because this is a two-sided test and Z = -2.05 is negative,
P-value:
P = 0.0404 < = 0.05.
c. The Null hypothesis should be rejected.
d. There is evidence to suggest that the percentage of supermarket shoppers who believe that the supermarket Ketchup was as good as the national brand Ketchup differs from 61%. Thus, the national brand Ketchup manufacturer should not be pleased with this conclusion, because the results cannot be applied to its own product.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.