AP Statistics: t-Inference

To test a claim about a mean, when the population standard deviation is unknown we use:

• z procedures
• Pythagorean Theorem
• t procedures
• np > 10 and n(1-p) > 10

Tags

CCSS.HSS.ID.A.4

What do we use to estimate unknown parameters?

• Hypothesis Test
• Confidence Interval
• Trig Identity
• Guess and check

You have an SRS of 23 observations from large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98% confidence interval for the mean of the population?

• 2.177

• 2.183

• 2.326

• 2.500

• 2.508

Tags

CCSS.HSS.ID.A.4

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content σ ?

• 90% confidence; n = 25 

• 90% confidence; n = 50 

• 95% confidence; n =25 

• 95% confidence; n =50 

• n=100 at any confidence level 

Tags

CCSS.HSS.IC.B.4

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 25 laboratory rats. A 95% confidence interval for the mean blood cholesterol level μ is 80.2 to 89.8. Which of the following would cause the most worry about the validity of this interval?

• There is a clear outlier in the data

• A stemplot of the data shows a mild right skew

• You do not know the population standard deviation σ

• The population distribution is not exactly Normal.

• None of these are a problem when using t-interval

Tags

CCSS.HSS.IC.B.4

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let p represent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confident level?

• 550

• 600

• 650

• 700

• 750

Tags

CCSS.HSS.IC.B.4

A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?” He asks listeners to phone in and vote “Yes” if they agree the drinking age should be lowered and “No” if not. Of the 100 people who phoned in, 70 answered “Yes.” Which of the following conditions for inference about a proportion using a confidence interval are violated?

I. The data are a random sample from the population of interest
II. n is so large that both n(phat) and n(1-phat) are at least 10
III. The population is at least 10 times as large as the sample

• I only

• II only

• III only

• I and II only

• I, II and III

Tags

CCSS.HSS.IC.B.4

How can you reduce both Type I and Type II errors?

• it can't be reduced
• redo the tests
• increase the sample size
• tamper with the data

What interval should be used?

• 2 Sample t interval for means

• Paired t interval

• Paired t test

• 1 proportion z interval

Tags

CCSS.HSS.IC.B.4

What test should be used?

• 2 proportion z test

• 1 proportion z test

• 2 sample t test for means

• 1 sample t test for mean

Tags

CCSS.7.SP.B.4