Statistics Assignment

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STAT200 Fall 2013

Each question is worth one point unless otherwise noted.

Be sure to show all your work for problems requiring calculations. Simply submitting answers for many problems is not enough to earn credit. Please highlight your final answer. All work must be your own. You should have knowledge of UMUC policies.

1. A study compared medication and chicken soup for subjects suffering from influenza. It was found that among 73 patients treated with medication, there was a 92% success rate. Among 83 patients treated with chicken soup, there was a 72% success rate. Calculations using those results showed this if there really is no difference in success rates between medication and chicken soup, then there is about 1 chance in 1000 of getting success rates like the ones obtained in this study.

a. Should we conclude that medication is better than chicken soup for influenza?

b. Does the result have statistical significance? Why or why not?

c. Does the result have practical significance?

d. Should medication be the recommended treatment for influenza?

2. What is the level of measurement for each of the following:

a. Monthly temperatures for Silver Spring, MD

b. Companies that produced movies in 2013

c. Rankings of horses in race

d. Salaries for statistics professors

3. What type of sampling is being used for each of the following:

a. The host of a radio station asks listeners to call in and give their opinions about DC statehood.

b. In order to estimate the percentage of defects, a manager selects every 23rd laptop that comes off the assembly line starting with the fifth one and continuing until she has 75.

c. I am being audited by the IRS. I was told that it was because I was randomly selected from all women in my age group.

4. The following data were collected on amounts of radon in basements in my development.

Radon Frequency

0.00 – 0.99

14

1.00 – 1.99

20

2.00 – 2.99

21

3.00 – 3.99

4

4.00 – 4.99

2

5.00 – 5.99

1

a. What is the class width?

b. What are the class midpoints?

c. What are the class boundaries?

d. Create a histogram for the data.

5. The following data show the number of students per grade level in a private pre K-8 charter school:

34 39 36 43 51 53 63 62 79 73

What is the 5-number summary?

Construct a boxplot for the data.

6. A simple random sample of the cost of laptops (in dollars) is as follows:

714 751 664 789 818 779 698 836 753 834 693 802

As of this writing, the average price was reported to be 678. Based on these results, is a laptop cost of 500 unusual? Why or why not? You need to base your answer on your calculated standard deviation, which needs to be given in your solution.

7. (Worth 2 points) In my third grade class, the heaviest child weights 92.95 pounds. The other children in the class have weights with a mean of 69.6 pounds and a standard deviation of 2.8 pounds.

a. What is the difference between the heaviest child and the mean weight of the other children?

b. How many standard deviations is that (the difference found in part (a))?

c. Convert the heaviest weight to a z-score.

d. Based on your answer to (c), does the heaviest child’s weight meet the criterion of being unusual? Why or why not?

8. (Worth 1.5 points) A survey was conducted asking people who they were going to vote for in the November presidential election. Participants were randomly selected. Data were then analyzed by how many participants in each age group responded. Results were as follows:

Age

18 – 21

22 – 29

30 – 39

40 – 49

50 – 59

60 +

Responded

73

255

245

136

138

202

Refused

11

20

33

16

27

49

a. What is the probability that the person selected was someone who is 60 and over who responded?

b. What is the probability that the selected person refused to respond or was over 59?

9. (Worth 1.5 points) I collected data from children in fourth grade and fifth grade with regard to their passing the Standards of Learning (SOL) assessment in my school district. The results are as follows:

Pass

Fail

Fourth Grade

201

288

Fifth Grade

126

224

a. What is the probability that one randomly selected child passed the SOL or was in fifth grade?

b. What is the probability that one randomly selected child did not pass the SOL or was in fifth grade?

10. (Worth 2 points) I asked the 100 children in my school which season was their favorite. The results are in the table below.

Summer

Winter

Fall

Spring

Boys

39

35

8

4

Girls

6

5

2

1

a. If 3 children are randomly selected, what is the probability that they are all girls and they all like fall best using replacement?

b. If 3 children are randomly selected, what is the probability that they are all girls and they all like fall best without using replacement?

c. Without replacement, what is the probability that 3 children are selected are boys who like spring best?

11. (Worth 1.5 points) Twenty students are eligible for free after-school tutoring. A simple random sample of five is selected.

a. How many different simple random selections are possible?

b. What is the probability of each simple random sample?

12. In a study of cigarette smoking, groups of 6 US households were randomly selected. In the table below, the random variable x represents the number of households among 6 that had a smoker living there.

x

P(x)

0

0.539

1

0.351

2

0.095

3

0.014

4

0.001

5

0+

6

0+

a. What is the mean?

b. What is the standard deviation?

c. Is this a probability distribution? Why or why not?

13. (Worth 2 points) A computer manufacturer claims that the chips it makes are so accurate that there is only a 1/2000 probability of getting a defective chip. A salesman at a local store purchased 5 chips and claimed that 2 of them were defective.

a. Find the probability of getting exactly 2 defective chips when buying 5 chips.

b. Find the probability of getting at least 2 defective chips when buying 5 chips.

c. Does the salesman’s claim of getting 2 defective chips seem valid? Explain.

14. (Worth 2 points) Psychologists frequently measure achievement using a test with scores that are normally distributed, with a mean of 100 and a standard deviation of 15.

a. What is the probability that a child I test has an achievement score >131.5?

b. What is the probability that a child I test has an achievement score between 110 and 120?

c. What is the achievement score separating the bottom 37% from the others?

15. (Worth 1.5 points) A large number of simple random samples of n = 85 are obtained from a large population of birth weights having a mean of 3420 g and a standard deviation of 495 g. The sample is calculated for each sample.

a. What is the approximate shape of the distribution of the sample means?

b. What is the expected mean of the sample means?

c. What is the expected standard deviation of the sample means?

STAT 200
Fall 2013

Each question is worth one point unless otherwise noted.

Be sure to show all your work for problems requiring calculations. Simply submitting answers
for many problems is not enough to earn credit. Please highlight your final answer. All work
must be your own.
You should have knowledge of

UMUC policies.

1.

A study

compared medication and
chicken soup

for subjects suffering from
influenza
. It
was found that among 73 patients treated with medication, there was a 92% success rate.
Among 83 patients treated with
chicken soup, there was a 72% success rate. Calculations
using those results showed this if there really is no difference in success rates between
medication and chicken soup, then there is about 1 chance in 1000 of getting success
rates like the ones obtained in this study.

a.

Should we conclude that medication i
s better than chicken soup for influenza?

b.

Does the result have statistical significance? Why or why not?

c.

Does the result have practical significance?

d.

Should medication be the recommended treatment for influenza?

2.

What is the level of
measurement for each of the following:

a.

Monthly temperatures for
Silver Spring, MD

b.

Compan
ies that produced movies in 2013

c.

Rankings of
horses in race

d.

Salaries for statistics professors

STAT 200 Fall 2013

Each question is worth one point unless otherwise noted.
Be sure to show all your work for problems requiring calculations. Simply submitting answers
for many problems is not enough to earn credit. Please highlight your final answer. All work
must be your own. You should have knowledge of UMUC policies.

1. A study compared medication and chicken soup for subjects suffering from influenza. It
was found that among 73 patients treated with medication, there was a 92% success rate.
Among 83 patients treated with chicken soup, there was a 72% success rate. Calculations
using those results showed this if there really is no difference in success rates between
medication and chicken soup, then there is about 1 chance in 1000 of getting success
rates like the ones obtained in this study.

a. Should we conclude that medication is better than chicken soup for influenza?

b. Does the result have statistical significance? Why or why not?

c. Does the result have practical significance?

d. Should medication be the recommended treatment for influenza?

2. What is the level of measurement for each of the following:

a. Monthly temperatures for Silver Spring, MD

b. Companies that produced movies in 2013

c. Rankings of horses in race

d. Salaries for statistics professors

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