# 0.2 Practice tests (1-4) and final exams  (Page 30/36)

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41 . As the degrees of freedom increase in an F distribution, the distribution becomes more nearly normal. Histogram F 2 is closer to a normal distribution than histogram F 1, so the sample displayed in histogram F 1 was drawn from the F 3,15 population, and the sample displayed in histogram F 2 was drawn from the F 5,500 population.

42 . Using the calculator function Fcdf, p -value = Fcdf(3.67, 1E, 3,50) = 0.0182. Reject the null hypothesis.

43 . Using the calculator function Fcdf, p -value = Fcdf(4.72, 1E, 4, 100) = 0.0016 Reject the null hypothesis.

## 13.4: test of two variances

44 . The samples must be drawn from populations that are normally distributed, and must be drawn from independent populations.

45 . Let ${\sigma }_{M}^{2}$ = variance in math grades, and ${\sigma }_{E}^{2}$ = variance in English grades.
H 0 : ${\sigma }_{M}^{2}$ ${\sigma }_{E}^{2}$
H a : ${\sigma }_{M}^{2}$ > ${\sigma }_{E}^{2}$

## Practice final exam 1

Use the following information to answer the next two exercises: An experiment consists of tossing two, 12-sided dice (the numbers 1–12 are printed on the sides of each die).

• Let Event A = both dice show an even number.
• Let Event B = both dice show a number more than eight

1 . Events A and B are:

1. mutually exclusive.
2. independent.
3. mutually exclusive and independent.
4. neither mutually exclusive nor independent.

2 . Find P ( A | B ).

1. $\frac{2}{4}$
2. $\frac{16}{144}$
3. $\frac{4}{16}$
4. $\frac{2}{144}$

3 . Which of the following are TRUE when we perform a hypothesis test on matched or paired samples?

1. Sample sizes are almost never small.
2. Two measurements are drawn from the same pair of individuals or objects.
3. Two sample means are compared to each other.
4. Answer choices b and c are both true.

Use the following information to answer the next two exercises: One hundred eighteen students were asked what type of color their bedrooms were painted: light colors, dark colors, or vibrant colors. The results were tabulated according to gender.

Light colors Dark colors Vibrant colors
Female 20 22 28
Male 10 30 8

4 . Find the probability that a randomly chosen student is male or has a bedroom painted with light colors.

1. $\frac{10}{118}\text{}$
2. $\frac{68}{118}\text{}$
3. $\frac{48}{118}\text{}$
4. $\frac{10}{48}\text{}$

5 . Find the probability that a randomly chosen student is male given the student’s bedroom is painted with dark colors.

1. $\frac{30}{118}\text{}$
2. $\frac{30}{48}\text{}$
3. $\frac{22}{118}\text{}$
4. $\frac{30}{52}\text{}$

Use the following information to answer the next two exercises: We are interested in the number of times a teenager must be reminded to do his or her chores each week. A survey of 40 mothers was conducted. [link] shows the results of the survey.

x P ( x )
0 $\frac{2}{40}\text{}$
1 $\frac{5}{40}\text{}$
2
3 $\frac{14}{40}\text{}$
4 $\frac{7}{40}\text{}$
5 $\frac{4}{40}\text{}$

6 . Find the probability that a teenager is reminded two times.

1. 8
2. $\frac{8}{40}\text{}$
3. $\frac{6}{40}\text{}$
4. 2

7 . Find the expected number of times a teenager is reminded to do his or her chores.

1. 15
2. 2.78
3. 1.0
4. 3.13

Use the following information to answer the next two exercises: On any given day, approximately 37.5% of the cars parked in the De Anza parking garage are parked crookedly. We randomly survey 22 cars. We are interested in the number of cars that are parked crookedly.

8 . For every 22 cars, how many would you expect to be parked crookedly, on average?

1. 8.25
2. 11
3. 18
4. 7.5

9 . What is the probability that at least ten of the 22 cars are parked crookedly.

1. 0.1263
2. 0.1607
3. 0.2870
4. 0.8393

10 . Using a sample of 15 Stanford-Binet IQ scores, we wish to conduct a hypothesis test. Our claim is that the mean IQ score on the Stanford-Binet IQ test is more than 100. It is known that the standard deviation of all Stanford-Binet IQ scores is 15 points. The correct distribution to use for the hypothesis test is:

1. Binomial
2. Student's t
3. Normal
4. Uniform

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