AP Statistics Unit 5

The proportion of orange salamanders along a certain stream is known to be 10%. Use a Normal model to approximate the probability that, for a sample of 100 salamanders along this stream, at least 20 of them are orange.

• .0004

• .3707

• .9996

• .6293

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.1

The manager of an orchard expects about 70% of his apples to exceed the weight requirement for "Grade A" designation. At least how many apples must he sample to be 90% confident of estimating the true proportion within ± 4%?

• 356

• 505

• 89

• 23

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. Is there a significant difference in the proportions of customers who favor soft-serve ice cream in the eastern and western parts of the state?

• There is a significant difference at the 0.10 level, but not at the 0.05 level.

• There is a significant difference at the 0.05 level, but not at the 0.01 level.

• There is a significant difference at the 0.01 level, but not at the 0.001 level.

• There is no significant difference at the 0.10 level.

With an alpha-level of 5%, what is the power of a test against an alternative for which the probability of a Type II error is 3%?

• 3%

• 97%

• 95%

• The power cannot be determined from the given information.

A major university expresses 95% confidence that about 90% to 93% of its students find employment in their field within one year of graduation. What is the margin of error implied in this statement?

• 1%

• 1.5%

• 3%

• 6%

Not wanting to risk poor sales for a new soda flavor, a company decides to run one more taste test on potential customers, this time requiring a higher approval rating than they had for earlier tests. This higher standard of proof will increase

I. the risk of Type I error

II. the risk of Type II error

III. power

• I only

• II only

• III only

• II and III

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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