Assignment:
1. A recent article in the Topeka Times reported that 40% of all farms in Kansas will have financial problems this year. A recent survey of 200 farms revealed that 66 of them had financial problems. At the α = 0.01 significance level can we conclude that a smaller proportion of farms actually have problems?
a. State the null and alternative hypothesis statements.
H0: EE
H1: EE
b. See the list of formulas at the end of this test to determine the appropriate formula that would be used to calculate the test statistic for this hypothesis test.
c. The test statistic was calculated to be -2.02, determine the p-value.
d. Determine the 99% confidence interval estimate of the proportion of Kansas farms that will have financial problems.
e. Given that the Topeka Times article's estimate of 40% of the farms will have financial problems was a good estimate, how large a sample should they have taken to have been 95% confident in their estimate within an error of 5%?
f. Interpret the results of the hypothesis test, decision and summary.
2. An office manager knows from long experience that 7 percent of the administrative staff will arrive late to work at least once this week.
a. What is the probability that in a sample of 15 staff members none will arrive late at least once this week?
b. What is the probability that in a sample of 15 staff members at least one will arrive late at least once this week?
3. A recent study of the cost per meal in family restaurants in the downtown New York City area were normally distributed with a mean of $18.00 and a standard deviation of $2.50.
a. If a single cost of a meal was selected at random what is the probability that the meal would cost less than $16.00?
b. If a sample of 5 meal costs were selected, what is the probability that the sample mean would be less than $16.00?
4. In your own words (please do not give me a quote from the textbook) write a paragraph explaining what the p-value is.
5. A large international retail chain is interviewing recent college graduates for potential positions with the company. Each graduate is rated as either below average, average or above average with respect to technical knowledge and each graduate is also rated with respect to his or her potential for advancement; fair, good, or excellent. These traits for 500 recent graduates are summarized in the following table.
|
|
Potential For Advancement
|
|
|
|
|
Technical Knowledge
|
Fair
|
Good
|
Excellent
|
Total
|
|
Bellow average
|
16
|
12
|
22
|
50
|
|
Average
|
45
|
60
|
45
|
150
|
|
Above average
|
93
|
72
|
135
|
300
|
|
Total
|
154
|
144
|
202
|
500
|
|
|
|
|
|
|
|
a. If a single recent graduate was selected at random what is the probability they would have technical knowledge or have excellent potential for advancement?
b. If a single recent graduate was selected at random what is the probability they would have above average technical knowledge and good potential for advancement?
c. If a single recent graduate was selected at random what is the probability they would have below average sales ability given they have good potential for advancement?
6. In your own words write a paragraph defining "Inferential Statistics".
7. A consumer organization wants to know whether there is a significant difference in the price of a particular model of portable cd players at three different types of stores. The price of the cd player was checked in a sample of 5 discount stores, 5 variety stores and 5 department stores. The results are shown below (all prices are in dollars). Test to see if there is a significant difference in the prices between the three types of stores using a significance level of α = 0.05. The test statistic for this test was calculated to be 13.38.
|
Discount
|
Variety
|
Department
|
|
12
|
15
|
19
|
|
13
|
17
|
17
|
|
14
|
14
|
16
|
|
12
|
18
|
20
|
|
15
|
17
|
19
|
a. State the null and alternative hypothesis statements.
H0: EE
H1: EE
b. Determine the critical value.
c. See the list of formulas at the end of this test to determine the appropriate formula that would be used to calculate the test statistic for this hypothesis test.
d. Interpret the results.
8. At a local pizza restaurant the owner believes that 50% of the customers will pay by cash, 25% will pay with a credit card and another 25% will pay with a personal check. The owner asked the manager to collect a random sample of two hundred customers to see their method of payment and test to see if the owner was correct, the survey results are below. Can it be concluded that the owner is correct? Use the significance level of α = 0.05.
|
|
Cash
|
Credit Card
|
Check
|
|
Frequency
|
112
|
48
|
40
|
a. State the null and alternative hypothesis statements.
H0: EE
H1: EE
b. Determine the critical value.
c. See the list of formulas at the end of this test to determine the appropriate formula that would be used to calculate the test statistic for this hypothesis test.
d. The test statistic was calculated to be 3.52, interpret the results.
9. In your own words, write a paragraph defining what a "Hypothesis Test" is. (Don't give me an example of one, nor tell me how to construct one; tell me what it is, its use, and its interpretations.)
10. A psychologist conducted a recent study to determine whether the fact that whether a student was left or right-handed was independent of their ability to perform will in a statistics class. The following are the results of the study. The test statistic for this test was calculated to be 18.18.
|
|
Handedness
|
|
Ability
|
Left
|
Right
|
|
Bellow average
|
40
|
52
|
|
Average
|
106
|
47
|
|
Above average
|
67
|
32
|
What is your conclusion using a significance level of α = 0.05
a. State the null and alternative hypothesis statements.
H0: EE
H1: EE
b. Determine the critical value.
c. See the list of formulas at the end of this test to determine the appropriate formula that would be used to calculate the test statistic for this hypothesis test.
d. Interpret the results.
11. The research department at the home office of New Haven Insurance conducts ongoing research on the causes of automobile accidents, the characteristics of the drivers and so on. A random sample of 400 policies written on single persons revealed 120 had at least one accident in the previous three-year period. Similarly, a sample of 600 policies written on married persons revealed that 150 had been in at least one accident. At the α = 0.05 level of significance, is there a significant difference in the proportions of single and married persons having an accident during the last three-year period? For this test, the test statistic was calculated to be -1.74.
a. State the null and alternative hypothesis statements.
H0: EE
H1: EE
b.See the list of formulas at the end of this test to determine the appropriate formula that would be used to calculate the test statistic for this hypothesis test.
c. Determine the p-value.
d. Interpret the results.
12. The director of the Atlanta office for Delta Airlines would like to compare the weights of checked baggage for families of four people and compare those weights between families who are traveling overseas for vacations against those families of four who are flying within the United States for vacation. She collected the following sample information:
Overseas Domestic
x = 142.50 ñb x = 130.25 lb
s = 12.25 lb s = 15.75 lb
n = 6 n = 7
The degrees of freedom for this comparison were calculated to be 10. At the α = 0.10
level of significance, can she conclude that the mean weights of the checked baggage for the
families flying overseas is greater than the weights of the families making domestic flights?
a. State the null and alternative hypothesis statements.
H0: EE
H1: EE
b. Determine the critical value.
c.See the list of formulas at the end of this test to determine the appropriate formula that would be used to calculate the test statistic for this hypothesis test.
d. The test statistic for this test was calculated to be 1.58, interpret the results.
13. At a General Electric refrigerator assembly plant, the director of human resources has noticed an increase in number of hours lost to on-the-job accidents. Four years ago, in an attempt to improve the situation, he began a safety awareness program in which employees heard safety announcements and suggestions during their lunch hour in the cafeteria. To evaluate the program, he selected a random sample of eight participants and found the number of hours each lost in the six months before the safety awareness program began and in the last six months. Below are the results. At the α = 0.05 significance level, can he conclude that the number of hours lost has declined?
|
Employee
|
Before
|
After
|
|
1
|
6
|
5
|
|
2
|
6
|
2
|
|
3
|
7
|
1
|
|
4
|
7
|
3
|
|
5
|
4
|
3
|
|
6
|
3
|
6
|
|
7
|
5
|
3
|
|
8
|
6
|
7
|
a. State the null and alternative hypothesis statements.
H0: EE
H1: EE
b. Determine the critical value.
c. See the list of formulas at the end of this test to determine the appropriate formula that would be used to calculate the test statistic for this hypothesis test.
d. The test statistic for this test was calculated to be -1.70, interpret the results.