Statistic mathematics

MATH 131 ELEMENTARY STATISTICS Practice Test Ch 8 – 10

NAME_________________________________________________________

Problems will require hypotheses, a claim, and whether there is evidence to support the claim.

1. (8 pts) We will use the critical value method to test the following hypothesis.

A sample of 40 Pre 1964 quarters have a mean weight of 6.193 grams with a population

standard deviation of .087 grams. A sample of 40 post 1964 quarters has a mean weight of

5.639 grams and a population standard deviation of .06194 grams. Use α = 0.05 to test the

claim the mean weight of quarters is lighter after 1964.

a. Set up the null and alternate hypothesis and identify the claim

b. Find the z-score value that bounds the critical region.

c. Find the test statistic z value using the formula 𝑧 = (𝑥1−𝑥2)

√ 𝜎1

2

𝑛1 +

𝜎2 2

𝑛2

d. Determine your conclusion concerning the hypothesis test and your claim using the

rejection region.

2. (6 pts) In a study about magnetic pain therapy, two groups of adults were questioned about

their pain levels. Use a calculator and α = 0.01 to test the claim that magnetic therapy doesn’t

help pain.

No magnets : n = 20, p = 0.45

Magnets: n = 20, p = 0.4

3. (6 pts) Below is the self-reported height versus the actual height of men in inches. Use a

calculator and α = 0.05 to test the claim that reported heights are taller than actual heights.

reported 69 71 63 70 71 60 65 64 54

actual 67.9 69.9 64.9 68.3 70.3 60.6 64.5 67 55.6

4. (6 pts) A teacher would like to test the claim that students that take tests without a proctor

score better than students that take a test with a proctor. A group of 30 students take a test

with a proctor and have a mean score of 74.3 % with a standard deviation of 12.87 %. A second

group of 32 students take the same exam and have a mean score of 88.62 % and a standard

deviation of 22.09 %. Use a calculator to test the claim that taking a test with a proctor results

in a lower mean score with α = 0.01 and data not pooled.

MATH 131 ELEMENTARY STATISTICS Practice Test Ch 8 – 10

5. (6 pts) The data below is of bill amounts and tip amounts at a restaurant. Use a calculator to

test the claim that there is positive linear correlation. If there is positive linear correlation, find

the equation of the regression line and use it to determine the bill if the tip is $12.50. Use

significance level of 0.05

Bill 33.46 50.68 87.92 98.84 63.6 107.34

Tip 5.5 5 8.08 17 12 16

6. (6 pts) The data below is of the number of people in a town and the number of deer counted in

the town. Use a calculator to test the claim that there is negative linear correlation using α =

0.05. If there is negative linear correlation, find the equation of the regression line and use it to

determine the number of people in a town where 50 deer are counted.

People 5000 125,000 20,000 10,000 90,000 50,000 25,000 8000 10,000

Deer 240 75 150 250 100 85 50 300 200

7. (8 pts) A researcher claims that the distribution of ages of movie goers is distributed as follows:

2 – 17 18 – 24 25 – 39 40 – 49 50 +

23% 20% 22% 9% 26%

1000 people are randomly selected and the observed frequency is given below:

2 – 17 18 – 24 25 – 39 40 – 49 50 +

240 209 203 106 242

Use a calculator and α = 0.01 to test the researchers claim.

8. (8 pts) The contingency table below shows the results of a random sample of students by school

location and the numbers of those students achieving basic skills in three subjects. Using a

calculator and α = 0.05, test the claim that the variables are independent. Explain what the

relationship that you found from this test means practically.

Reading Math Science

Urban 43 40 38

Suburban 63 66 61