Chapter 10 AP Statistics

At a baseball game, 42 of 65 randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34 of 52 randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90% confidence interval for the difference in population proportions(game − concert) is (−0.154, 0.138). Which of the following gives the correct outcome of the researcher’s test of the claim?

• Because the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same.
• Because the center of the interval is –0.008, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.
• Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.
• Because the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

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 p₂₀₁₂– p₂₀₀₉ is (approximately)

• 0.075 ± 0.085
• 0.075 ± 0.071
• 0.075 ± 0.043

 In a simple random sample of 100 cars of a certain popular model in 2010, 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 2011, it was found that 50 had the same defect. Let p₁ and p₂ be the proportions of all cars of this model in 2010 and 2011, respectively, that have the defect. We wish to test H₀ : p₁ - p₂ = 0 against H_A : p₁ - p₂ > 0 . Which of the following is closest to the P-value for this test?

• 0.0418
• 0.0536
• 0.0268

A manufacturer receives parts from two suppliers. An SRS of 400 parts from Supplier 1 contains 20 defective parts, while an independent SRS of 100 parts from Supplier 2 contains 10 defective parts. Let p₁ and p₂ be the proportions of defective parts made by Supplier 1 and Supplier 2, respectively. Is there evidence of a significant difference in the proportions of defective parts made by these two suppliers? To answer this question, you test the hypotheses H₀ : p₁ - p₂ = 0 against H_A : p₁ - p₂  ≠ 0 . Which of the following is closest to the P-value of the test?

• 0.9398
• 0.0602
• 0.0301

A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...

• The sample size is too small for a z-distribution
• Clarity ratings for the entire bacth are normally distributed.  
• The t-distribution will create a narrower interval than z.
• The standard deviation for the batch is unknown.

Which of the following does NOT have an affect on the width of a confidence interval?

• Sample mean

• Sample size

• Sample standard deviation

A __________ gives an interval of plausible values for the _____________. 

• confidence interval, statistic
• point estimate, parameter
• point estimate, statistic
• confidence interval, parameter

What is the format for interpreting a confidence interval? 

• The interval from ___ to ___ captures the true mean in context.
• C% of samples of the same size taken from the same population will capture the parameter in question
• There is convincing evidence that C% gives the interval (___, ___) capturing the parameter in question.
• We are C% confident that the interval from ___ to ___ captures the [parameter in context].

What can you do to reduce the margin of error? 

• increase the confidence level
• decrease the confidence level
• increase sample size
• decrease sample size

What is the critical value z* for a 99% confidence interval? 

• -2.58
• 1.96
• -1.64
• 2.58