## STATISTICS 200 Assume the weights of men are normally

Assume the weights of men are normally distributed with a mean of 170 lbs and a standard
deviation of 30 lbs. Show all work. Just the answer, without supporting work, will receive no
credit.

(a)
(b)

Find the 75th percentile for the distribution of men’s weights.
What is the probability that a randomly selected man weighs more than 200 lbs

2.
(a)
(b)

Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500
and a standard deviation of 100. Show all work. Just the answer, without supporting work, will
If a random sample of 64 test scores is selected, what is the standard deviation of the sample
mean?
What is the probability that 64 randomly selected test scores will have a mean test score that is
between 475 and 525?

3.

A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a
90% confidence interval estimate of the proportion of adults believing in global warming. Show
all work. Just the answer, without supporting work, will receive no credit.

4.

In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were
treated with garlic tablets. Cholesterol levels were measured before and after the treatment. The
changes in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14.
Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after the
garlic tablet treatment. Show all work. Just the answer, without supporting work, will receive
no credit.

5.

Mimi is interested in testing the claim that banana is the favorite fruit for more than 50% of the
adults. She conducted a survey on a random sample of 100 adults. 58 adults in the sample
chose banana as his / her favorite fruit.
Assume Mimi wants to use a 0.10 significance level to test the claim.

(a)

Identify the null hypothesis and the alternative hypothesis.

(b)

Determine the test statistic. Show all work; writing the correct test statistic, without supporting
work, will receive no credit.
Determine the P-value for this test. Show all work; writing the correct P-value, without
supporting work, will receive no credit.
Is there sufficient evidence to support the claim that banana is the favorite fruit for more than
50% of the adults? Explain.

(c)
(d)

6.

In a study of freshman weight gain, the measured weights of 5 randomly selected college
students in September and April of their freshman year are shown in the following table.

Student
1
2
3
4
5

Weight (kg)
September
April
67
66
53
55
64
68
71
70
70
75

Is there evidence to suggest that the mean weight of the freshmen in April is greater than the

mean weight in September?

Assume we want to use a 0.10 significance level to test the claim.
(a)

Identify the null hypothesis and the alternative hypothesis.

(b)

Determine the test statistic. Show all work; writing the correct test statistic, without supporting
work, will receive no credit.
Determine the P-value for this test. Show all work; writing the correct P-value, without
supporting work, will receive no credit.
Is there sufficient evidence to support the claim that the mean weight of the freshmen in April
is greater than the mean weight in September? Justify your conclusion.

(c)
(d)

7.

In a pulse rate research, a simple random sample of 40 men results in a mean of 80 beats per
minute, and a standard deviation of 11.3 beats per minute. Based on the sample results, the
researcher concludes that the pulse rates of men have a standard deviation greater than 10 beats
per minutes. Use a 0.05 significance level to test the researcher’s claim.

(a)

Identify the null hypothesis and alternative hypothesis.

(b)

Determine the test statistic. Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
Determine the P-value for this test. Show all work; writing the correct P-value, without
supporting work, will receive no credit.
Is there sufficient evidence to support the researcher’s claim? Explain.

(c)
(d)

8.

The UMUC Daily News reported that the color distribution for plain M&M’s was: 40%
brown, 20% yellow, 10% orange, 10% green, and 20% tan. Each piece of candy in a random
sample of 100 plain M&M’s was classified according to color, and the results are listed below.
Use a 0.05 significance level to test the claim that the published color distribution is correct.
Show all work and justify your answer.
Color
Number

Brown
42

Yellow
21

Orange
12

Green
7

Tan
18

(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic,
without supporting work, will receive no credit.
(c) Determine the P-value. Show all work; writing the correct P-value, without supporting
work, will receive no credit.
(d) Is there sufficient evidence to support the claim that the published color distribution is

9.

A STAT 200 instructor believes that the average quiz score is a good predictor of final exam
score. A random sample of 5 students produced the following data where x is the average quiz
score and y is the final exam score.
x
y

(a)
(b)

80
145

50
150

60
130

100
180

70
120

Find an equation of the least squares regression line. Show all work; writing the correct
equation, without supporting work, will receive no credit.
Based on the equation from part (a), what is the predicted final exam score if the average quiz
score is 90? Show all work and justify your answer.