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STAT_200_full_Homework_Solutions
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STAT 200 full Homework Solutions
The complete homework assignment included 30 questions that are reproduced below. Please note that tables have not been rendered correctly from the scanned text.
STATISTICS HOMEWORK
Refer to the following table for Questions 1, 2, and 3.
The table shows temperatures on the first 12 days of October in small town in Maryland.
DATE Temperature DATE Temperature DATE Temperature
Oct 1 73 Oct 5 53 Oct 9 62
Oct 2 66 Oct 6 53 Oct 10 49
Oct 3 66 Oct 7 62 Oct 11 52
Oct 4 70 Oct 8 55 Oct 12 57
1. Determine the five number summary for this data.
2. Determine the mean temperature.
3. Determine the mode(s), if any.
Refer to the following situation for Questions 4, 5, and 6.
Consider the following distribution by age groups.
AGE FREQUENCY RELATIVE FREQUENCY
10-14 0.04
15-19
20-24 10
25-29 6
30-34 5
35-39 4
40-44 2
45-49 1
TOTAL 50 1.00
4. Complete the table.
5. Is this distribution bell-shaped, skewed to the left, or skewed to the right? Explain your
answer.
6. In what age range is the median? Explain your answer.
7. Your entire gold coin collection consists of 5 coins. Their weights are 2, 3, 8, 7, and 6
oz. respectively. Find the standard deviation of their weights. Show all work.
Refer to the following information for Questions 8 and 9.
In a recent survey, participants were asked which Apple products influenced them the most.
IPOD IPHONE IPAD TOTAL
Age under 20 70 100 130 300
Age 20-40 160 140 90 390
Age over 40 190 110 50 350
Total 420 350 270 1040
8. What is the probability that the participant was aged 20-40 or was influenced by iPad the
most?
9. What is the probability that the participant was influenced by iPod the most, given that
the participant is aged under 20?
Refer to the following information for Questions 10 and 11.
A club has 30 members.
10. How many different ways are there to assign the roles of President, Vice President, and
Treasurer?
11. How many different committees of size 4 can be formed?
_____________________________________________________________________________________
12. The Island Club is holding a fund-raising raffle. Ten thousand tickets have been sold for
$2 each. There will be a first prize of $3,000, three second prizes of $1,000 each, five
third prizes of $500 each, and 20 consolation prizes of $100 each. What are the expected
net winnings? Interpret your answer.
_____________________________________________________________________________________
Questions 13 and 14 involve the random variable x with probability distribution given below.
x -2 4 5 6 7
P(x) 0.15 0.05 0.3 0.1 0.4
13. Determine the expected value of x.
14. Determine the standard deviation of x.
Questions 15, 16, and 17 involve the following situation.
A random variable X is binomial with n = 15 and p = 0.2.
15. What is the probability that X=4?
16. What is the probability that X is at least 2?
17. What is the expected value of X? What is the standard deviation of X?
Refer to the following information for Questions 18, 19, 20, and 21.
The weights of the 100 boys in Boy Scout Troop 829 are normally distributed with a mean
of 170 pounds and a standard deviation of 5 pounds.
18. What is the probability that a boy picked at random weighs less than 165 pounds?
19. How many boys would you expect to weigh between 161 and 173 pounds?
20. Find the 96th percentile.
21. Find the cutoff values which represents the middle 80% of their weights.
Refer to the following information for Questions 22, and 23.
A random sample of 94 light bulbs had a mean life of x¯ = 587 hours. The standard
deviation of the lifetime of all such light bulbs is of o = 36 hours.
22. Construct a 90% confidence interval estimate of the mean life, µ, of all light bulbs of this
type.
23. It was expected that the mean lifetime of the light bulbs was 600 hours. Do the results
contradict expectations? Explain your answer.
24. Consider the hypothesis test given by
H0 : µ = 50
H1 : µ > 50
In a random sample of 100 subjects, the sample mean is found to be x¯ = 53.4. Also, the
population standard deviation is o = 8
Determine the P-value for this test. Is there sufficient evidence to justify the rejection of
H0 ? Explain.
25. We perform the following hypothesis test of proportion of successes in a population.
H0 : p = 0.7 vs. H2 : p < 0.7.
In a sample of 100 items, we discover 63 successes.
What is the conclusion at the ? = 0.05 level? Explain your answer.
26. Given a sample size of 18, with sample mean 660.3 and sample standard deviation 95.9,
we perform the following hypothesis test.
H0 : µ = 700
H1: µ ? 700
What is the conclusion of the test at the ? = 0.05 level? Explain your answer.
Use the data in the table to answer Questions 27 and 28.
x 3 1 4 4 5
y 2 -2 5 4 8
27. Find the equation of the regression line. Show all work.
28. Find the predicted value of y when x = 4.
29. A worker in an insurance company processes claims. The distribution of the number of
claims processed each day in a week of this worker’s life is as follows.
Day # of Claims
Monday 28
Tuesday 45
Wednesday 40
Thursday 23
Friday 29
The worker’s boss thinks the worker’s claims processing is sporadic and is not evenly
distributed throughout the week. At the a = 0.05 level, is there sufficient evidence to
conclude that the worker’s claims processing is sporadic?
Show all work – include the hypotheses, the computation of the test statistic, state the
critical value, and state the conclusion of the test.
30. Below is a compilation of student distribution in our four statistics classes from the
summer of 2009.
Course STAT 200 STAT 225 STAT 230 STAT 250
Percentage 45.8 12.0 32.8 9.4
The enrollment report for the summer of 2011 is given as follows.
Course STAT 200 STAT 225 STAT 230 STAT 250
Frequency 249 71 133 47
At the 1% significance level, do the data provide sufficient evidence to conclude that
2011’s enrollment distribution differs from the 2009 distribution?
Show all work – include the hypotheses, the computation of the test statistic, state the critical value, and state the conclusion of the test.
About the Solutions
The answers to Question 13, 14, and 17 are reproduced below. Please purchase the full solutions if you wish to use them.
13. Determine the expected value of x.
x P(x) x*P(x)
-2 0.15 -0.3
4 0.05 0.2
5 0.3 1.5
6 0.1 0.6
7 0.4 2.8
Mean 4.8
The expected value is found by adding the x*P(x) column. The calculated expected value is 4.8
14. Determine the standard deviation of x.
Answer:
x P(x) x*P(x) (x-mean)^2 * P(x)
-2 0.15 -0.3 6.936
4 0.05 0.2 0.032
5 0.3 1.5 0.012
6 0.1 0.6 0.144
7 0.4 2.8 1.936
Stan Dev 3.009983389
The standard deviation is found by taking the “square root” of the summation of the column: (x-mean)^2*P(x)
Here the calculated standard deviation is 3.00998
17. What is the expected value of X? What is the standard deviation of X?
Expected Value= 15*.2
=3
Standard Deviation= Squareroot(15*.2*.8)
=1.549
Question Files
STAT HWK.docx
STAT_200_full_Homework_Solutions.pdf
Other Details about the Project/Assignment
Subjects
:
Mathematics -> Statistics
Topic
:
Homework assignment for College Statistics class STAT 200
Level
:
College / University
Tags
:
Homework assignment, College Statistics, STAT 200
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Project Details
Question Files
STAT HWK.docx
STAT_200_full_Homework_Solutions.pdf
Subjects
:
Mathematics -> Statistics
Topic
:
Homework assignment for College Statistics class STAT 200
Level
:
College / University
Tags
:
Homework assignment, College Statistics, STAT 200
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