1)
Of 92 adults selected randomly from one town, 61 have health insurance through the ACA. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance through the ACA.
2)
A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with σ = 19.0 milligrams. Construct a 95% confidence interval for the true mean cholesterol content, µ, of all such eggs.
3)
A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the standard deviation, σ, of the scores of all subjects.
4)
The daily intakes of milk (in ounces) for ten randomly selected people were:
23.3 28.4 10.5 16.4 26.418.1 20.4 17.3 27.4 13.2
Use SPSS to find a 99% confidence interval for the population standard deviation σ.
5)
A hypothesis test is performed to test the claim that a population proportion is greater than 0.7. Find the probability of a type II error, β, given that the true value of the population proportion is 0.72. The sample size is 50 and the significance level is 0.05.
6)
Random samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below.
Model A / Model B / Model C / Model D23 / 28 / 30 / 25
25 / 26 / 28 / 26
24 / 29 / 32 / 25
26 / 30 / 27 / 28
Use SPSS to test the claim that the four different models have the same population mean. Use a significance level of 0.05.
7)
The following data shows annual income, in thousands of dollars, categorized according to the two factors of gender and level of education. Assume that incomes are not affected by an interaction between gender and level of education. Use SPSS to test the null hypothesis that gender has no effect on income. Use a 0.05 significance level.
Female / MaleHigh School / 23, 27, 24, 26 / 25, 26, 22, 24
College / 28, 36, 31, 33 / 35, 32, 39, 28
Graduate Degree / 41, 38, 43, 49 / 35, 50, 47, 44
8)
A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. Construct a 99% confidence interval for the difference between the two population proportions. Assume that the samples are independent and have been randomly selected.
9)
A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below and the population of paired differences can be assumed to be normally distributed. Construct a 95% confidence interval for the mean difference between the before and after scores.
Before / 74 / 83 / 75 / 88 / 84 / 63 / 93 / 84 / 91 / 77After / 73 / 77 / 70 / 77 / 74 / 67 / 95 / 83 / 84 / 75
10)For randomly selected adults, IQ scores are normally distributed with a standard deviation of 15. The scores of 14 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of IQ scores of college students is less than 15. Round the sample standard deviation to three decimal places.
115 128 107 109 116 124 135
127 115 104 118 126 129 133
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