AP Stats - Chapter 10 Test

Choosing to run a test with a lower risk of α,that is, a smaller level of significance, results in

• a lower risk of Type II error and lower power.

• a lower risk of Type II error and higher power.

• a higher risk of Type II error and lower power.

• a higher risk of Type II error and higher power.

• no change in risk of Type II error or in power.

A factory manager would like to compare two different assembly techniques by looking at the average number of units assembled by an employee during a certain time period. The manager uses random selection to choose 200 employees from the factory, and randomly assigns each employee to one of the two techniques. After training the employees on their respective techniques, the manager records the number of units each of the employees

assembles within the allotted time. Which of the following would be the most appropriate inferential statistical test

in this situation?

• One-sample z-test

• Two-sample t-test

• Paired t-test

• One-sample t-test

• None of these tests are appropriate

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CCSS.HSS.ID.A.4

Which of the following statements is (are) true about the t-distribution with k degrees of freedom?

I. The t-distribution is symmetric.

II. The t-distribution with k degrees of freedom has a smaller variance than the t- distribution with k + 1 degrees of freedom.

III. The t-distribution has a larger variance than the standard normal (z) distribution.

• I only

• II only

• III only

• I and II

• I and III

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CCSS.HSS.ID.A.3

In an attempt to estimate the mean carbon content of the day's steel output, an engineer chooses a random sample of 15 rods from that day. The process is newly

developed, and there are no historical data on the variability of the process, although graphic displays of the engineer's sample results indicate no heavy skew or outliers. In estimating this day's mean

carbon content, the primary reason the engineer should use a t-confidence interval rather than a z-

confidence interval is because the engineer

• is estimating the population mean using the sample mean.

• is using the sample variance as an estimate of the population variance.

• is using data, rather than theory, to judge that the carbon content is normal.

• is using data from a specific day only.

• has a small sample, and a z-confidence interval should never be used with a small sample.

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CCSS.HSS.IC.B.4

It is appropriate to use a t-distribution with 20 degrees of freedom for which of the following?
I. Constructing a confidence interval from an SRS with n = 19.

II. Doing a hypothesis test where $H_o:\ \mu_1-\mu_2=0\$  and $H_a:\ \mu_1-\mu_2>0$  with $n_1=8$  and $n_2=12$  .
III. Testing for differences between two proportions where $n_1=21$  and $n_2=29$  

• I only

• II only

• III only

• I, II, and III

• None are appropriate

What is the critical t-value for finding a 96 percent confidence interval estimate from a sample of 18

observations?

• 2.054

• 2.205

• 2.214

• 2.224

• 2.235

A relief fund is set up to collect donations for the families affected by recent storms. A random sample of 400 people shows that 28% of the 200 who were contacted by telephone actually made contributions, compared to only 18% of the 200 who received first class mail requests. Which formula calculates the 95% confidence interval for the difference in the proportions of people who make donations if contacted by telephone or first class mail?

• $\left(0.28-0.18\right)\pm1.96\sqrt{\frac{\left(0.23\right)\left(0.77\right)}{200}}$

• $\left(0.28-0.18\right)\pm1.96\sqrt{\frac{\left(0.23\right)\left(0.77\right)}{200}+\frac{\left(0.23\right)\left(0.77\right)}{200}}$

• $\left(0.28-0.18\right)\pm1.96\sqrt{\frac{\left(0.23\right)\left(0.77\right)}{400}}$

• $\left(0.28-0.18\right)\pm1.96\sqrt{\frac{\left(0.28\right)\left(0.72\right)}{200}+\frac{\left(0.18\right)\left(0.82\right)}{200}}$

• $\left(0.28-0.18\right)\pm1.96\sqrt{\frac{\left(0.28\right)\left(0.72\right)}{400}+\frac{\left(0.18\right)\left(0.82\right)}{400}}$

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CCSS.HSS.IC.B.4

A philosophy professor wants to find out whether the mean age of the men is his large lecture class is different from the mean age of the women in his classes. After collecting data from a random sample of his students, the professor tested the hypothesis $H_o:\ \mu_M-\mu_W=0$  against the alternative $H_a:\ \mu_M-\mu_W\ne0$ .  The p-value for the test was 0.003.  Which is true?

• There is a 0.3% chance that the mean ages for the men and women are equal

• There is a 0.3% chance that the mean ages for the men and women are different

• It is very unlikely that the professor would see results like these if the mean age of men was equal to the mean age of women

• There is a 0.3% chance that another sample will give these same results

• There is a 99.7% chance that another sample will give these same results

A test for physical fitness is to be performed at two different sites. At one test site subjects taking the test for a second time volunteered to inhale supplemental oxygen for 10 minutes before the test. In fact, some received oxygen, but others (randomly assigned) were given just normal air. Test results showed that 42 of 66 subjects who breathed oxygen improved their performance on the fitness test, compared to only 35 of 63 students who did not get the oxygen. Which testing procedure should we use to test whether breathing extra oxygen can help improve fitness test results?

• 1-proportion z-test

• 2-proportion z-test

• 1-sample t-test

• 2-sample t-test

• matched pairs t-test

At one vehicle inspection station, 13 of 52 trucks and 11 of 88 cars failed the emissions test. Assuming these vehicles were representative of the cars and trucks in that area, what is the standard error of the difference in the percentages of all cars and trucks that are not in compliance with air quality regulations?

• 0.025

• 0.032

• 0.049

• 0.070

• 0.095