Question

4) Brad Davenport, a consumer reporter for a national cable TV channel, is working on a story evaluating generic food products and comparing them to their brand-name counterparts. According to Brad, consumers claim to like the brand-name products better than the generics, but they can’t even tell which is which. Notice that if a person can not tell the difference, they would have a 50-50 chance of identifying the brand-name chip. So if more than half the people can identify the brand-name potato chip, there are people who can tell the difference. a) State the Hypothesis to show some people can identify the brand-name potato chip. b) Choose a level of a. Use a = 0.025 for this problem. c) To test his theory, Brad gives each of 200 consumers two potato chips – one generic, the other a brand name – and asks them which one is the brand-name chip. The data appear in the Potato Chip worksheet of the HW1 data workbook on Moodle. Collect data and calculate necessary statistics to test the hypothesis. d) Sketch the sampling distribution. Include the critical value and test statistic e) Draw a conclusion and report that in the problem context.

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Answer 1

(a)

Let p be the proportion of people who can identify the brand-name potato chip.

Null hypothesis H0: p = 0.5

Alternative hypothesis H1: p > 0.5

(b)

Let $\alpha$ = 0.025 for this problem.

(c)

Here the data is given only for 50 people. You can modify the answer is you have data of 200 people.

n = 50

Number of people who were Correct = 26

Observed proportion $\hat{p}$ = 26/50 = 0.52

Standard error of sampling distribution of proportion = $\sqrt{p * (1-p)/n } = \sqrt{0.5 * (1-0.5)/50 } = 0.07071068$

Test Statistic, z = ($\hat{p}$ - p) / SE = (0.52 - 0.5) / 0.07071068 = 0.2828

P-value = P(z > 0.2828) = 0.3886

(d)

Sampling distribution of proportion is Normal distribution with mean = 0.5 and standard deviation of 0.07071068.

Critical value for $\alpha$ = 0.025 is z = 1.96

Critical value for proportion to reject H0 = 0.5 + 1.96 * 0.07071068 = 0.6386

(e)

As, p-value is greater than the significance level of 0.025, we fail to reject H0 and conclude that there is no statistically significant evidence that proportion of people who can identify the brand-name potato chip is greater than 0.5. Thus, there is no statistically significant evidence that some people can identify the brand-name potato chip