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Statistics Problem Set: Hypothesis Testing

1. What is the difference in average daily hotel room rates between Minneapolis and New Orleans? Suppose we want to estimate this difference by taking hotel rate samples from each city and using a 98% confidence level. The data for such a study follow. Use these data to produce a point estimate for the mean difference in the hotel rates for the two cities. Assume the population variances are approximately equal and hotel rates in any given city are normally distributed

Minneapolis
n = 22
average = $112
s = $11

New Orleans
n = 20
average = $122
s = $12
2. Use the data given to test the following hypotheses (? = .05). Assume the differences are normally distributed in the population.

Ho: D = 0 Ha: D does not equal 0

Individual Before After
1 107 102
2 99 98
3 110 100
4 113 108
5 96 89
6 98 101
7 100 99
8 102 102
9 107 105
10 109 110
11 104 102
12 99 96
13 101 100

3. Does age make a difference in the amount of savings a workers feels is needed to be secure at retirement? A study by CommSciences for Transamerica Asset Management found that .24 of workers in the 25-33 age category felt that $250,000-$500,000 is enough to be secure at retirement. However, .35 of the workers in the 34-52 age category feel that this amount is enough. Suppose 210 workers in the 25-33 age category and 176 workers in the 34-52 age category were involved in this study. Use these data to construct a 90% confidence interval to estimate the difference in population proportions on this question.

4. How long are resale houses on the market? One survey by the Houston Association of Realtors reported that in Houston, resale houses are on the market an average of 112 days. Of course, the length of time varies by market. Suppose random samples of 13 houses in Houston and 11 houses in Chicago that are for resale are traced. The data shown here represent the number of days each house was on the market before being sold. Use the given data and a 1% level of significance to determine whether the population variances for the number of days until resale are different in Houston than in Chicago. Assume the number of days resale houses are on the market are normally distributed.

Houston
132 126
138 94
131 161
127 133
99 119
126 88
134

Chicago
118 56
85 69
113 67
81 54
94 137
93.

Solution Preview

1. At degree of freedom of 40 (22+20-2=40), the critical value for 98% confidence interval is 2.423. (it could be found by using TINV(0.02,40), TINV is a function in EXCEL).
mean difference=122-112=10
standard error=sqrt(((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2))*sqrt(1/n1+1/n2)=sqrt(((22-1)*11^2+(20-1)*12^2)/(22+20-2))*sqrt(1/22+1/20)=
3.548639
margin of error=critical value*standard error=2.423*3.548639=8.6
The upper limit: 10+8.6=18.6
The lower limit: 10-8.6=1.4
Therefore, the 98% confidence interval for the ...

Solution Summary

The solution discusses a statistics problems set including hypothesis testing.

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