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Statistics and Hypothesis Testing Problems

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1. True or False? A hypothesis test is a process that uses population parameters to test a claim
about about a sample statistics.
2. Use the given statement to represent a claim. Write its complement and state which is Ha and which is H0.
3. Determine whether the hypothesis test with the given null hypothesis listed below is lefttailed, right-tailed, or two-tailed.
H0 : = 100
Use the following information to answer questions 4-7.
Working Hours A company's shipping department claims that the average working hours per
week is greater than 44 hours.
4. Write the null hypothesis, H0.
5. Write the alternate hypothesis, Ha.
6. Which hypothesis is the claim?
7. What type of hypothesis test will be required?
Use the following information to answer questions 8 and 9.
Internet Users A study claims that the proportion, p, of adults in the United States that use
the internet is 68%.
8. Write a sentence describing a type I error for a hypothesis test of the claim above.
9. Write a sentence describing a type II error for a hypothesis test of the claim above.
Use the following information to answer questions 10 and 11.
Shipment Weights A postal worker claims that the average weight of all U.S. Postal parcel
shipments is greater than 5:6 pounds. Assume that a hypothesis test is conducted.
10. With regard to the claim, how should you interpret a decision that rejects the null hypothesis?
11. With regard to the claim, how should you interpret a decision that fails to reject the null
hypothesis?
Use the following information pertaining to a hypothesis test to answer questions 12 and
13. Test: right-tailed, z = 2:27,
= 0:01
12. Find the P-value for the hypothesis test.
13. Decide whether to reject H0 for the given level of significance
.
14. Suppose that a two-tailed hypothesis test is being conducted and the P-value is 0:0768. What
are the z-values that corresponds to this P-value?

15. Find the critical value for the indicated type of test and level of significance
.
Test: Left-tailed,
= 0:10.
Use the following information to answer questions 16-19.
Suppose that for a two-tailed hypothesis test the critical values are z0 = 1:88 and z0 =
1:88. State whether you would reject or fail to reject the null hypothesis if the standardized
test statistic z has the values listed below.
16. z = 1:72
17. z = 2:03
18. z = 1:65
19. z = 1:80
20. Test the claim about the population mean at the given level of significance
using the
given sample statistics. Claim: < 1000;
= 0:05; Sample statistics: x = 988, s = 29,
n = 50.
Section 7.3
For problems 21 and 22, use the value of
and n to and the critical value t0 for the
specified t-test.
21. Test: Left-tailed;
= 0:025; n = 17
22. Test: Two-tailed;
= 0:01; n = 23
23. Use a t-test to test the claim about the population mean at the given level of significance

using the given sample statistics.
Claim: = 640 6

= 0:05
Sample statistics: x = 643, s = 4:0, n = 10.

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Solution Preview

1. True or False? A hypothesis test is a process that uses population parameters to test a claim
about a sample statistics.
False. The right one is a hypothesis is a process that uses sample statistics to test a claim about the value of a population parameter.
2. Use the given statement to represent a claim. Write its complement and state which is
Ha and which is H0.
238
Ho: the mean expenditure in the gas for a family is 238 dollars.
Ha: the mean expenditure in the gas for a family is not 238 dollars.
3. Determine whether the hypothesis test with the given null hypothesis listed below is lefttailed, right-tailed, or two-tailed.
H0 : = 100
This is two tailed since it gives no direction.
Use the following information to answer questions 4-7.
Working Hours A company's shipping department claims that the average working hours per
week is greater than 44 hours.
4. Write the null hypothesis, H0.
Ho Null hypothesis: the average working hours per week is equal or less than 44 hours. µ<=44.
5. Write the alternate hypothesis, Ha.
Ha: the average working hours per week is greater than 44 hours. µ>44
6. Which hypothesis is the claim?
Ha is the claim.
7. What type of hypothesis test will be required?
Since it is directional, it is one tailed (right tailed) t test.
Use the following information to answer questions 8 and 9.
Internet Users A study claims that the proportion, p, of adults in the United States ...

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Statistics : Hypothesis Testing, T-tests, One-Tailed and Two-Tailed Tests (12 Problems)

For each of the following problems, be sure to specify the null hypothesis being tested, and whether you will use a t test for independent samples or a t test for nonindependent samples; also, specify whether you will use a one-tailed or two-tailed test.

1. In a study designed to discover whether men or women drink more coffee, a researcher (working on a very limited budget) observes five men and five women randomly selected from her university department. Here's what she found:

Number of Cups of Coffee
In 1 Day at Work

Men Women
5 8
1 3
4 7
2 3
3 5

(a) Run the appropriate test, assuming that both men and women were originally part of one random sample, with n = 10, and were then divided into men's and women's groups.
(b) Use the same data, but this time assume that the men were randomly selected and then women were selected so that each man could be matched with a woman of the same age, job classification, and overall health status.

2. Using hospital and agency records, you locate six pairs of identical twins, one of whom was adopted at birth and the other of whom was in foster care for at least 3 years. All the twins are now 5 years old. You want to show that early adoption leads to better intellectual ability, so you test all the twins with the Wechsler Intelligence Scale for Children (WISC). Your results are as follows:

WISC Score
Twin Pair No. Adopted Twin Foster-Care Twin
1 105 103
2 99 97
3 112 105
4 101 99
5 124 104
6 100 110

3. The following table contains scores on an index of depression for three groups of clients at a college counseling center. Group 1 clients have received six sessions of counseling; group 2 clients were put on a waiting list for 6 weeks and asked to keep a personal journal during that time; group 3 clients were put on the waiting list with no other instructions. Use a t test to decide whether:
(a) group 2 (journal) clients scored differently from group 3 (control) clients.
(b) Group 1 (counseled) clients scored differently from group 2 (journal) clients.
(c) Group 1 (counseled) clients scored higher than group 3 (control) clients.

Group 1 Group 2 Group 3
(counseled) (journal) (control)
22 6 8
16 10 6
17 13 4
18 13 5
8 2
4
4. A researcher tests that high-frequency hearing acuity of a group of teens 2 days before they attend a rock concert; 2 days after the concert, she tests them again. Here are her results; she hopes to show that the teens hear better before the concert than afterward (the higher the score on this test, the poorer the hearing).

Subject Scores Scores
(Preconcert) (Postconcert)
Tom 12 18
Dan 2 3
Sue 6 5
Terri 13 10
Karen 10 15
Lance 10 15
Christy 5 6
Jan 2 9
Lenora 7 7
Roberta 9 9
Dave 10 11
Victoria 14 13

5. Cindy, who has had several autumn outings spoiled by bad weather, is convinced that it rains more on weekends than on weekdays in the fall. To test this hypothesis, she randomly selects 10 weekdays and 10 weekend days from the last fall, and finds out how much rain fell on each. Her data follow. (With such small numbers, roundoff errors can make a big difference. Best carry your work in this problem out to four places, instead of the usual two.)

Rainfall on Weekdays Rainfall on Weekend Days
0 .5
.3 0
.2 0
0 0
.15 .2
0 0
0 .1
0 .07
.05 0
.03 .12

6. Do dogs who are fed twice a day eat more in the morning or more in the evening? Here are the data from 15 healthy pets; what do you conclude?

Dog Morning Feeding (oz) Evening Feeding (oz)
Rover 5.9 5.8
Spot 9.9 7.6
Zachary 1.3 1.9
Cagney 8.6 7.2
Clem 7.1 7.3
Claudia 6.0 4.2
Johann S. Bark 7.3 7.2
Tigger 3.3 3.2
Beelzebub 11.9 10.0
Whiskers 5.4 5.2
Him 8.8 9.0
Chiggers 6.9 6.3
Sam 6.5 6.5
Lucy 5.4 5.1
Frisky 5.8 7.2

7. You really are interested in dogs, so you decide to test another hypothesis: Male dogs generally eat more than females. In the data in Problem 6, Rover, Spot, Zachary, Clem, Johann Bark, Beelzebub, Him, and Sam are males. Is your hypothesis supported?

8. The registrar at Cow Catcher College is interested in the relationship between academic achievement and early choice of major. She randomly selects 20 students from the sophomore class at CCC, and records their GPAs and whether they've decided on a major yet. Given the following data, what can she conclude?

GPA When GPA When
Major Is Chosen Major Not Chosen
3.5 3.2
3.1 2.5
2.9 2.0
4.0 3.7
3.8 1.5
3.2 2.9
3.7 3.4
3.5 3.3
2.9
3.4
3.6
3.0

1. A researcher is interested in differences among blondes, brunettes, and redheads in terms of introversion/extroversion. She selects random samples from a college campus, gives each subject a test of social introversion, and comes up with the following:

Blondes Brunettes Redheads
5 3 2
10 5 1
6 2 7
2 4 2
5 3 2
3 5 3

Use a simple ANOVA to test for differences among the groups.

2. A (hypothetical!) study of eating patterns among people in different occupations yielded the following:

Bus Drivers College Professors U.S. Presidents
(N = 10) (N = 10) (N = 4)
Mean junk food score 12 17 58.3

Source df Sum of squares Mean square F

Between 2 6505 3252.5 6.1**
Within 21 11197 533.2

(a) What do you conclude?
(b) Perform the appropriate post-hoc analysis.

3. Farmer Hensh suspects that his chickens like music, because they seem to lay more eggs on days when his children practice their band instruments in the hen house. He decided to put it to a scientific test, and records the number of eggs collected each day for a month, along with the music provided on that day:

No Music Mary (Piccolo) Benny (Clarinet) Satchmo (Trumpet)
11 12 35 52
26 17 42 78
31 19 31 16
18 25 33 41
15 32 44 25
27 40 55
30 57
64
20
22
73
25
What does he conclude, and how does he explain it?

4. The college librarian at Harton University has been keeping track of who checks out library books. After 6 months of collecting data, he performed an ANOVA, scribbling his results on a sheet of paper. Unfortunately, his dog got into his brief-case and what you see below is all that could be resurrected. Assuming that his calculations were accurate, what could you conclude from his research? Draw a graph of the group means to make your explanation clear:

This is the librarian's sheet of paper:

Compare # of books used by Math majors, psych majors, education majors. Divide each into graduate students (G) and undergraduate (U).

Group means look good __

Math Psych Education
Undergrad. 15 13 7
Grad. 8 42 26

Source df SS MS f
Major 2 ___ ___ 7.82
Level (u/g) 1 ___ ___ 8.33
Interaction (MxL) 2 ___ ___ 9.77
Within Groups 344 ___ ___ ___

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