Chapter 12 MC Review

In a population of bats living in a certain region, 30 percent have a wingspan greater than 10 inches. In a random sample of 80 bats living outside of the region, 20 had a wingspan greater than 10 inches. Consider a one-sample z-test to investigate whether there is evidence that the proportion of bats with a wingspan greater than 10 inches living outside the region is different from that of the bats living in the region. Which of the following is the correct test statistic?

• $z=\frac{0.30-0.25}{\sqrt{\frac{\left(0.25\right)\left(0.75\right)}{80}}}$

• $z=\frac{0.30-0.25}{\sqrt{\frac{\left(0.30\right)\left(0.70\right)}{80}}}$

• $z=\frac{0.25-0.30}{\sqrt{\frac{\left(0.25\right)\left(0.75\right)}{80}}}$

• $z=\frac{0.25-0.30}{\sqrt{\frac{\left(0.25\right)\left(0.75\right)}{80}}}$

• $z=\frac{0.25-0.30}{\sqrt{\frac{\left(0.30\right)\left(0.70\right)}{80}}}$

For a certain brand of canned corn, the company claims that the mean weight of the contents of the cans is 15.25 ounces. A random sample of 36 cans were selected. The sample was found to have mean 15.18 ounces and standard deviation 0.12 ounce. A hypothesis test will be conducted to investigate whether there is evidence to support the belief that the mean is less than 15.25 ounces. Which of the following is the correct test statistic for the hypothesis test?

• $t=\frac{15.18-15.25}{\frac{0.12}{6}}$

• $t=\frac{15.18-15.25}{\frac{0.12}{36}}$

• $t=\frac{15.25-15.18}{\frac{0.12}{6}}$

• $t=\frac{15.25-15.18}{\frac{0.12}{36}}$

• $t=\frac{15.25-15.18}{0.12}$

The process of producing pain-reliever tablets yields tablets with varying amounts of the active ingredient. It is claimed that the average amount of active ingredient per tablet is at least 200 milligrams. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The mean content of the active ingredient for this sample is 194.3 milligrams, while the standard deviation is 21 milligrams. What is the approximate p-value for the appropriate test?

• 0.012

• 0.024

• 0.050

• 0.100

• 0.488

In order to make statistical inferences when testing a population proportion p , which of the following conditions verify that inference procedures are appropriate?

1. The data are collected using a random sample or random assignment.

2. The sample size is less than 10 percent of the population size.

3. np₀ ≥10 and n(1-p₀) ≥ 10 for sample size and hypothesized proportion .

• I only

• II only

• III only

• II and III only

• I, II, and III

A recent study reported the mean body mass index (BMI) for adults in the United States was 26.8. A researcher believes the mean BMI of marathon runners is less than 26.8. A random sample of 35 marathon runners had a mean BMI of 22.7 with a standard deviation of 3.1. The researcher will conduct a one-sample -test for a population mean. Have the conditions for inference been met?

• Yes, all conditions have been met.

• No, because the sample was not selected using a random method.

• No, because marathon runners are not a representative sample of all adults in the United States.

• No, because the shape of the distribution of the sample is not known.

• No, because the sample size is not large enough to assume normality of the sampling distribution of the sample mean.

Consider a population with population proportion p, and a sample from the population with sample proportion p-hat. Which of the following describes the purpose of the one-sample z-test?

• To estimate the value of p-hat

• To estimate the value of p

• To estimate a margin of error for p-hat

• To estimate the probability of observing a value as extreme as p-hat given p

• To estimate the probability of observing a value as extreme as p given p-hat

Tags

CCSS.HSS.IC.B.4

The distribution of mass for United States pennies minted since 1982 is approximately normal with mean 2.5 grams. A random sample of 10 pennies minted since 1982 was selected. The sample had a mean mass of 2.47 grams and a standard deviation of 0.04 gram. The test statistic for the population mean has which of the following distributions?

• A normal distribution with mean 0 and standard deviation 1

• A normal distribution with mean 2.5 and standard deviation 0.04

• A normal distribution with mean 2.47 and standard deviation 0.04

• A t -distribution with 9 degrees of freedom

• A t - distribution with 10 degrees of freedom

For a one-sample test for a population proportion p and sample size n, why is it necessary that np₀ and n(1-p₀) are both at least 10 ?

• The sample size must be large enough to support an assumption that the distribution of the population is approximately normal.

• The sample size must be large enough to support an assumption that the distribution of the sample is approximately normal.

• The sample size must be large enough to support an assumption that the sampling distribution of the sample proportion is approximately normal.

• The sample size must be large enough to support an assumption that the observations are independent.

• The sample size must be large enough to support an assumption that the sample proportion is an unbiased estimator of the population proportion.