Ripoff Coffee Co. sells coffee in cans that they promise contain a minimum of 2 pounds. U. R. Busted, an inspector for
the FTC [Federal Trade Commission], takes a sample of 42 cans to see if they actually contain at least 2 lbs at a .0102
level of significance. His sample results: x-bar = 1.92 lb with σ = .22 lb. What will U.R. find?
n = 42
μ= 2
0.22
x-bar = 1.92
(1) Formulate the hypotheses:
Ho: μ  2
Ha: μ < 2
(2) Decide the test statistic and the level of significance:
z (Left-tailed), α = 0.0102
Critical z- score = -2.3189
(3) State the decision Rule:
Reject Ho if z < -2.3189
(4) Calculate the value of test statistic:
SE = /n = 0.0339
z = (x-bar - μ)/SE = -2.3566
(5) Compare with the critical value and make a decision:
Since -2.3566 < -2.3189 we reject Ho and accept Ha
Decision: It appears that the claim that there is minimum of 2 pounds of coffee is not valid
In recent years, 22 percent of the American made automobiles sold in the United States were manufactured by General
Motors, 24 percent by Ford, 6 percent by Daimler-Chrysler, and 48 percent by all others. A sample of the sales of
American-made automobiles conducted last week revealed that 36 were manufactured by Daimler Chrysler, 220 by
Ford, 125 by GM, and 345 by all others. Do these observations fit with the expected values at a .01 level of significance?
Recorded Expected (Recorded - Expected)^2 / Expected
125 159.72 7.55
220 174.24 12.02
36 43.56 1.31
345 348.48 0.03
Chi-square = 20.91
Count = 4
α = 0.01
(1) Formulate the hypotheses:
Ho: The distribution is as per the expectation
Ha: The distribution is not as per the expectation; that is, it is different
(2) Decide the test statistic and the Critical value:
Chi-square
Degrees of freedom = 3
Critical Value = 11.3449
(3) State the decision Rule:
Reject Ho if Chi-square > 11.3449
(4) Calculate the value of test statistic:
Chi-square value = 20.9120
(5) Compare with the critical value and make a decision:
Since 20.9120 > 11.3449 we reject Ho and accept Ha
Decision: It appears that the distribution is not as per the expectation; It is different.
A recent MBA graduate, who is not too bright, is trying to decide between two job offers, one in Trenton and one in
Maui. DUH! One factor affecting his decision is the cost of a new home in each city. A recent study sampled 66 new
home sales in the Trenton area and found that the mean selling price of a new home was $176,900 with a population
standard deviation of $59,000. A similar Maui study based on a sample of 54 new home sales found that the mean
selling price was $198,500 with a population standard deviation of $49,800. Conduct a test at the .034 level of
significance to determine if there is any real difference in the mean selling price of new homes in these two cities.
n1 = 66
n2 = 54
x1-bar = 176900
x2-bar = 198500
59000
49800
(1) Formulate the hypotheses:
Ho: μ1 = μ2
Ha: μ1 ≠ μ2
(2) Decide the test statistic and the level of significance:
z (Two-tailed), α = 0.034
Lower Critical z- score = -2.1201
Upper Critical z- score = 2.1201
(3) State the decision Rule:
Reject Ho if |z| > 2.1201
(4) Calculate the value of test statistic:
SE = {(1^2 /n1) + (2^2 /n2)} = 9933.2316
z = (x1-bar -x2-bar)/SE = -2.1745
(5) Compare with the critical value and make a decision:
Since 2.1745 > 2.1201 we reject Ho and accept Ha
Decision: It appears that the home prices are significantly different.