Critical thinking
December 5, 2018
Calculus II – Spring 2014
December 5, 2018

6. (TCO C) A company contemplating the introduction of a new product wants to estimate the percentage of the market that this new product might capture. In a survey, a random sample of 100 potential customers were asked whether they would purchase this new product. The results were that 14 responded affirmatively.

a. Compute the 95% confidence interval for the population proportion of potential customers that would purchase the new product.
b. Interpret this confidence interval.
c. How many potential customers should be sampled in order to be 95% confident of being within 1% of the population proportion of potential customers that would purchase the new product? (Points : 18)

Question 7.7. (TCO D) According to Information Resources Inc., based on sales of teeth-cleaning products, Crest toothpaste controlled a 31.2% share of the market. A researcher from a rival company believes that this figure is high, and that in fact, Crest controls less than 31.2% of the market. A simple random sample of 400 consumers yields 116 use Crest. Does the sample data provide evidence to conclude that the researcher from the rival company is correct (with a = .05)? Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide evidence to conclude that Crest’s market share is below 31.2% (with a = .05)? (Points : 24)

Question 8.8. (TCO D) The R. R. Bowker Company of New York collects information on the retail prices of collectible children’s books and publishes its findings in Publisher’s Weekly. Last year, the mean retail price of collectible children’s books was $35.44. A random sample of 40 collectible children’s books (published this year) is selected, the retail prices are noted, and the results are as follows:

Sample Size: 40
Sample mean: $38.75
Sample standard deviation: $7.35

Does the sample data provide evidence to conclude that the mean retail price of collectible children’s books has increased over last year (using a = .10)? Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does this sample data provide evidence (with a = 0.10), that the mean retail price of collectible children’s books has increased over last year? (Points : 24)

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