SOLUTION: Easy Eye, Inc. manufactures adult sunglasses of all types. The company�s management is not sure whether to target the next promotional campaign primarily toward men or women and ha

Question 140734: Easy Eye, Inc. manufactures adult sunglasses of all types. The company�s management is not sure whether to target the next promotional campaign primarily toward men or women and has asked the research team to determine whether the market for sunglasses is split in half. A study is conducted at various cooperating stores selling sunglasses scattered throughout the market area. In a random sample of 300 adult purchasers of sunglasses, 141 were men.

If "Pi" is the proportion of adult sunglass purchasers who are men, what is the appropriate null hypothesis for Easy Eye, Inc. to test?
a. H0: Pi = 0.5
b. H0: Pi "not equal to" 0.5
c. H0: Pi >= 0.5
d. H0: Pi <= 0.5

What is the value of the test statistic?
a. �0.06
b. �0.50
c. �1.04
d. �2.54

Based on the data and at "a" = 0.05, what can Easy Eye�s management conclude?
a. An equal proportion of men and women are buying sunglasses in the market area.
b. A greater proportion of women buy sunglasses than do men in the market area.
c. A greater proportion of men buy sunglasses than do women in the market area.
d. There is not an equal proportion of men and women buying sunglasses in the market area.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Easy Eye, Inc. manufactures adult sunglasses of all types. The company�s management is not sure whether to target the next promotional campaign primarily toward men or women and has asked the research team to determine whether the market for sunglasses is split in half. A study is conducted at various cooperating stores selling sunglasses scattered throughout the market area. In a random sample of 300 adult purchasers of sunglasses, 141 were men.
If "Pi" is the proportion of adult sunglass purchasers who are men, what is the appropriate null hypothesis for Easy Eye, Inc. to test?
a. H0: Pi = 0.5
b. H0: Pi "not equal to" 0.5
c. H0: Pi >= 0.5
d. H0: Pi <= 0.5
Ans: "split in half" implies Ho: Pi = 0.5
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What is the value of the test statistic?
a. �0.06
b. �0.50
c. �1.04
d. �2.54
z(131/300) = (0.47-0.5)/sqrt[0.5*0.5/300] = -1.03923...
Ans: c
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Based on the data and at "a" = 0.05, what can Easy Eye�s management conclude?
p-value = 2P(-10 < z < -1.03923) = 2*0.14935... = 0.2987
a. An equal proportion of men and women are buying sunglasses in the market area.
b. A greater proportion of women buy sunglasses than do men in the market area.
c. A greater proportion of men buy sunglasses than do women in the market area.
d. There is not an equal proportion of men and women buying sunglasses in the market area.
Ans: Since the p-value is greater than 5%, fail to reject Ho;
Ans: a
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Cheers,
Stan H.

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