Question

 

A study showed that 62% 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 is less than 62%.

H₀: p < 0.62

H_a: p ≥ 0.62

H₀: p = 0.62

H_a: p ≠ 0.62

    

H₀: p > 0.62

H_a: p ≤ 0.62

H₀: p ≤ 0.62

H_a: p > 0.62

H₀: p ≥ 0.62

H_a: p < 0.62

(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?

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

(c)

At

α = 0.05,

what is your conclusion?

Do not reject H₀. There is sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%

.Do not reject H₀. There is insufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%.   

Reject H₀. There is sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%

.Reject H₀. There is insufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%.

(d)

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

Yes, the national brand ketchup manufacturer should be pleased with this conclusion. The results of the hypothesis test did not indicate that the percentage of shoppers who believe that supermarket ketchup is as good as the national brand ketchup was less than the overall percentage for all products.

No, the national brand ketchup manufacturer should not be pleased with this conclusion. The results of the hypothesis test indicated that the percentage of shoppers who believe that supermarket ketchup is as good as the national brand ketchup was less than the overall percentage for all products.   

Yes, the national brand ketchup manufacturer should be pleased with this conclusion. The results of the hypothesis test indicated that the percentage of shoppers who believe that supermarket ketchup is as good as the national brand ketchup was less than the overall percentage for all products.

No, the national brand ketchup manufacturer should not be pleased with this conclusion. The results of the hypothesis test did not indicate that the percentage of shoppers who believe that supermarket ketchup is as good as the national brand ketchup was less than the overall percentage for all products.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.62
Alternative Hypothesis, Ha: p ≠ 0.62

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.51 - 0.62)/sqrt(0.62*(1-0.62)/100)
z = -2.27

P-value Approach
P-value = 0.0116

As P-value < 0.05, reject the null hypothesis.

Reject H0. There is sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%

d)
No, the national brand ketchup manufacturer should not be pleased with this conclusion. The results of the hypothesis test indicated that the percentage of shoppers who believe that supermarket ketchup is as good as the national brand ketchup was less than the overall percentage for all products.