A local retailer is determining which of two brands of latex paint to carry. As

Question

A local retailer is determining which of two brands of latex paint to carry. As one component in their decision-making process, they are interested in determining if the amount consumers are willing to pay for a gallon of paint differs between the two varieties, on average. They conduct a survey in which they contact previous customers and ask them how much they would spend to purchase a gallon of each paint variety. The customers contacted were chosen by collecting a copy of all sales receipts at that location, recording contact information for the corresponding consumer in an Excel worksheet, scrambling the Excel worksheet randomly, and contacting the 100 customers at the top of the resulting list. From the resulting data, they were able to determine the following:

1. The average amount those surveyed would pay for variety A was $30 per gallon.
2. The average amount those surveyed would pay for variety B was $35 per gallon.
3. 71% of those surveyed prefer variety B to variety A.
4. 90% of those surveyed were male.
5. The average income of those surveyed was $90,000 per year.

---Based on the description above, which of the following best describes the data collection method implemented?

A. A simple random sample.

B. A census.

C. A systematic random sample.

D. A random sample, but not one discussed in class.

E. Not a random sample.

----Based on the above description, which of the following best describes the parameter of interest?

A. The proportion of customers that prefer variety A to variety B.

B. The difference between variety A and variety B in the average amount customers would pay.

C. The average amount customers are willing to pay for paint.

D. The amount customers are willing to pay for each type of paint.

E. All customers that shop the store.

---Let ?? represent the parameter of interest for this study. Based on the description above, which of the following alternative hypotheses best captures the question of interest?

A. H1:?>5H1:?>5

B. H1:?=5H1:?=5

C. H1:??5H1:??5

D. H1:?>0H1:?>0

E. H1:??0H1:??0

F. H1:?=0H1:?=0

---Based on the description above, which of the following conclusions is most appropriate?

A. Though the sample is representative, we are unable to make any conclusions about the statistic's relationship to the parameter.

B. The difference in the average price consumers are willing to pay in the varieties should be close to $5.

C. The difference in the average price consumers are willing to pay in the varieties is exactly $5.

D. The sample is biased because the percent of males represented is 90%.

---Based on the above description, which of the following generalizations is most appropriate?

A. Every customer will pay exactly $5 more for variety B.

B. On average, customers are willing to pay a bit more for variety A.

C. Every customer will pay more for variety B, though the amount may not be 5$.

D. On average, consumers are willing to pay a bit more for variety B.

Explanation / Answer

1. Option A.A simple random sample

2. Option B. The difference between variety A and variety B in the average amount customers would pay.

3. Option E. H1:??0H1:??0

4. Option B. The difference in the average price consumers are willing to pay in the varieties should be close to $5.

5. Option D. On average, consumers are willing to pay a bit more for variety B.

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