Statistics Unit 5

In the diagram, Region II is the rejection region for the null hy­pothesis. The area of which non-overlapping region(s) represents the probability of committing a Type II Error?

• Region I and Region III

• Region I and Region V

• Region II

• Region II and Region IV

Owners of a chain of ice cream shops recently examined sales figures and noticed that on a randomly selected day, 21 of 103 ice cream cus­tomers from their shop located in the eastern part of the state ordered soft-serve ice cream, while 29 of 132 ice cream customers from their shop located in the western part of the state ordered soft-serve ice cream. Construct a 95% confidence interval to find the difference in proportions of customers who favor soft-serve ice cream in the two parts of the state.

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For a simple random sample of 100 cars of a certain popular model in 2012, it was found that 20 had a certain minor defect in the brakes. For an independent SRS of 400 cars of the same model in 2009, it was found that 50 had the same defect. A 90% confidence interval for the difference between 2012 and 2009 is

• 0.075 ± 0.085

• 0.075 ± 0.071

• 0.075 ± 0.043

• 0.075 ± 0.142

In a simple random sample of 100 households in 2000, 43 had some credit card debt. In another simple random sample of 150 households in 2012, 72 had some credit card debt. Which of the following is the correct test statistic for testing the hypothesis H₀ : p_{2012 =} p₂₀₀₀ , that there is no difference in the proportion of households with credit card debt in these two years?

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• 3.6

• 10.6

• 51

• Cannot be determined without the actual data.

• 158 ± 21.3

• 158 ± 19.8

• 158 ± 21.2

• 158 ± 22.1

• 1400 ± 79.4

• 1400 ± 76.2

• 1400 ± 77.8

• 1400 ± 38.9

The margin of error for our 99% CI would stay the same

• The margin of error for our 99% CI would stay the same

• The margin of error for our 99% CI would decrease.

• The margin of error for our 99% CI would increase.

• None are true.

• 0.18 ± 0.023

• 0.18 ±0.0306

• 0.90 ± 0.0195

• 0.18 ± 0.0195

• ≈5700

• ≈9610

• ≈850

• ≈2400