Q: A random sample of 27 people has a mean commute time to work of $$34.3$$ minutes and a standard deviation of $$7.2$$ minutes. What is the margin of error for a $$95\%$$ confidence interval for the population mean? (Use $$z^* = 1.96)$$

$$E = 1.96 \times \dfrac{7.2}{\sqrt{27}} \approx 2.72$$

Q: Suppose the regression equation for a data set is $$y = 56.7 - 3.2x. $$What is the predicted value of $$y$$ when $$x = 2.5$$?

$$y = 56.7 - 3.2 \times 2.5 = 48.7$$

Question 1

A survey of 12,863 women in a country found that 47.3% received an influenza vaccine for a recent flu season. Which of the following best describes the population in this study?

Accepted Answer

All women in the country

Question 2

Which of the following variables is quantitative?

Accepted Answer

The number of cars owned by a household

Question 3

A simple random sample is best described as:

Accepted Answer

A sample where every possible group of a given size has an equal chance of being selected

Question 4

A double-blind experiment is used in clinical trials primarily to:

Accepted Answer

Reduce the placebo effect

Question 5

Given the following class limits for a frequency distribution: 40–47, 48–55, 56–63, 64–71, 72–79, what is the class width?

Accepted Answer

$$8$$

Question 6

The numbers of regular season wins for 12 football teams are: 2, 9, 15, 13, 12, 8, 13, 9, 11, 8, 6, 11. What is the range of this data set?

Accepted Answer

$$15 - 2 = 13$$

Question 7

Suppose the mean age in a city is $$27$$ years with a standard deviation of $$3.3$$ years. An age of $$33$$ years corresponds to a z-score of:

Accepted Answer

$$z = \dfrac{33 - 27}{3.3} = 1.82$$

Question 8

If $$P(A) = 0.3$$ and $$P(B) = 0.5$$ and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.8$$

Question 9

A probability distribution for the number of televisions per household in a small town is given by $$P(1) = 0.15$$, $$P(2) = 0.28$$, $$P(3) = 0.32$$, $$P(4) = 0.25. $$What is the probability that a randomly selected household has at least two televisions?

Accepted Answer

$$0.28 + 0.32 + 0.25 = 0.85$$

Question 10

Find the area under the standard normal curve between $$z = -2.00$$ and $$z = 3.00.$$

Accepted Answer

$$0.9786$$

Question 11

A population has a mean $$\mu = 27$$ and standard deviation $$\sigma = 24. $$What is the standard deviation of the sampling distribution of the sample mean for samples of size $$n = 36$$?

Accepted Answer

$$\sigma_{\bar{x}} = \dfrac{24}{\sqrt{36}} = 4$$

Question 12

A random sample of 27 people has a mean commute time to work of $$34.3$$ minutes and a standard deviation of $$7.2$$ minutes. What is the margin of error for a $$95\%$$ confidence interval for the population mean? (Use $$z^* = 1.96)$$

Accepted Answer

$$E = 1.96 	imes \dfrac{7.2}{\sqrt{27}} \approx 2.72$$

Question 13

A study finds that $$68\% of $$adults say they have started paying bills online in the last year. What is the point estimate for the population proportion?

Accepted Answer

$$\hat{p} = 0.68$$

Question 14

Given the hypotheses $$H_0$$: \mu = 8.2$$ and H_1$: \mu 
eq 8.2$$, what type of test is this?

Accepted Answer

Two-tailed test

Question 15

Suppose you want to test the claim that the mean price of a certain stock is more than $336. State the null and alternative hypotheses.

Accepted Answer

$$H_0$$: \mu = 336$$, H_1$: \mu \u003e 336$$

Question 16

A recent survey found that $$85\% of $$college students used student loans to pay for college. Let $$p be $$the proportion of college students who used student loans. What are the null and alternative hypotheses to test if the proportion is less than $$0.88$$?

Accepted Answer

$$H_0$$: p = 0.88$$, H_1$: p \u003c 0.88$$

Question 17

Given the following data for altitude (in thousands of feet) and speed of sound (in feet per second): as altitude increases, speed of sound tends to:

Accepted Answer

Decrease

Question 18

If the sample correlation coefficient $$r = -0.872$$ for a data set with $$n = 11$$, what does this indicate about the relationship between the two variables?

Accepted Answer

There is a strong negative linear correlation

Question 19

Suppose the regression equation for a data set is $$y = 56.7 - 3.2x. $$What is the predicted value of $$y$$ when $$x = 2.5$$?

Accepted Answer

$$y = 56.7 - 3.2 	imes 2.5 = 48.7$$

MAT 120 Final Exam Study Guide: Comprehensive Statistics Review

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