AP Stats Inference Method

One reason for using a t distribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that

• z can be used only for large samples

• z requires that you know the population standard deviation

• z requires that you can regard your data as an SRS from the population

• z requires that the sample size is at most 10% of the population size

• a z critical value will lead to a wider interval than a t critical value

A researcher wants to find a confidence interval estimate of the mean time it takes to complete an order over the phone at a call center for a large retail company. He has selected a random sample of 18 orders and recorded the time to complete the order. The sample mean time was 4.27 minutes and the sample standard deviation was 0.78 minutes. Assuming the conditions needed for inference are met, which of the following is the appropriate 98% confidence interval?

• 4.27 ± 2.326 ⋅ (0.78/√18)

• 4.27 ± 2.054 ⋅ (0.78/√18)

• 4.27 ± 2.552 ⋅ (0.78/√18)

• 4.27 ± 2.567 ⋅ (0.78/√18)

• 4.27 ± 2.567 ⋅ (0.78/√17)

Which of the following would not decrease the width of a confidence interval?

• I only

• II only

• III only

• I and II only

• II and III only

In a study of 150 accidents that required treatment in an emergency room, 36% involved children under 6 years of age.  Find the 90% confidence interval of the true proportion of accidents that involve children under the age of 6.

• 0.331 - 0.413

• 0.275 - 0.433

• 0.295 - 0.425

• 0.255 - 0.455

At a particular college, 78% of all students are receiving some kind of financial aid.The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?

•  78% is a population and 72% is a sample.

• 72% is a population and 78% is a sample

• 78% is a parameter and 72% is a statistic

• 72% is a parameter and 78% is a statistic

What does this symbol represent?

• population proportion

• parameter

• sample proportion

• population sample

A survey of a random sample of 2500 adults who have a credit card found that 570 had a balance of $1000 or more on their credit card.

What symbol would you use to describe the parameter?

• μ

• p

• p̂

• x̄

A 95% confidence interval for µ based on 𝑛 = 15 observations from a Normal population is (–0.73, 1.92). If we use this confidence interval to test the hypothesis 𝐻₀: 𝜇 = 0 against 𝐻_a: 𝜇 ≠ 0, what is the appropriate conclusion?

​ (a)   H₀ at the α = ​ (b)  

• fail to reject

• reject

• .05

• .10

Answer explanation

Because the hypothesized value, 0, is one of the plausible values in the 95% confidence interval, we fail to reject 𝐻₀:𝜇 = 0 at the α = 0.05 level.

You are thinking of conducting a one-sample 𝑡 test about a population mean 𝜇 using a 0.05 significance level. Which of the following statements is correct?

• You can carry out the test only if the population standard deviation is known.

• You can safely carry out the test if there are no outliers, regardless of the sample size.

• You can safely carry out the test if your sample size is at least 30.

• You can carry out the test if a graph of the data shows no strong skewness, regardless of the sample size.

• You should not carry out the test if the sample does not have a Normal distribution.

Answer explanation

We cannot use 𝑡 procedures if the graph of the sample data shows strong skewness OR outliers.

Which of the following has the smallest probability?

• 𝑃(𝑧>2) if 𝑧 is a standard Normal random variable.

• 𝑃(𝑡>2)if 𝑡 has 2 degrees of freedom.

• 𝑃(𝑧<2) if 𝑧 is a standard Normal random variable.

• 𝑃(𝑡<2) if 𝑡 has 5 degrees of freedom.

• 𝑃(𝑡>2)if 𝑡 has 5 degrees of freedom.

Answer explanation

The standard Normal distribution has less area in the tail than a 𝑡 distribution with df = 2 or df = 5.