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Stat 230Homework Assignment Week #6-SolutionsName:

You must answer each and every part in the order given and in the space provided.

Don’t leave anything blank.

Each numbered problem is worth 3 points for a total of 6 points for the assignment.

1. California and New York lead the list of average teachers’ salaries. Random samples of 45 teachers from each state yielded the following:

California / New York
Sample mean / 64,510 / 62,900
Population Standard Deviation / 8,200 / 7,800

At α = 0.10 test the claim that there is a difference in means of the salaries.

a. State the Hypotheses:

b.Compute theTest statistic:(Round off correctly)

c. Find the p-value:

d. Make the decision using the Decision Rule: (Compare the p-value withα)

e. Write the Conclusion (in plain English as related to the claim):

2. There is concern about the percent of on-time flights. A recent survey of two major airlines yielded the following results. At α = 0.05 test the claim that there is a difference in proportions of on-time flights.

Blue Airline / Red Airline
No. of flights / 300 / 250
No. of on-time flights / 213 / 200

a. State the Hypotheses:

b. Compute theTest statistic: (Round off correctly)

c. Find the p-value:

d. Make the decision using the Decision Rule: (Compare the p-value withα)

e. Write the Conclusion (in plain English as related to the claim):

2. The national sleep foundation used a survey to determine whether hours of sleeping per night are independent of age. The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individual’s age 50 and older

Hours of sleep

Age Fewer than 6 6 to 6.9 7 to 7.9 8 or more total

49 or younger 38 60 77 65 240

50 or older 36 57 75 92 260

  1. Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use a+.05. What is the p-value, and what is your conclusion?
  2. What is your estimate of the percentage of people who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, And 8 or more hours on weeknights?

Please solve those first #1 to 2.

1. A die is rolled 360 times. The results are shown in the table:

No / 1 / 2 / 3 / 4 / 5 / 6 / Total
O -Frequency / 55 / 48 / 67 / 51 / 73 / 66
(E-Frequency)

At the level of significance α = 0.05, do these results support the hypothesis that the die is balanced? What kind of Chi-Square test is this?

2. A random sample of car accidents for each day of the week for a year in a certain area showed the following results:

Day / Sun / Mon / Tue / Wed / Thu / Fri / Sat / Total
Number / 31 / 20 / 20 / 22 / 22 / 29 / 36
Expected frequency

Test the claim that accidents occur with equal frequency on the different days of the week.

Use α = 0.05. What kind of Chi-Square test is this?

3. There is a claim that fatal DWI crashes are mostly due to Weekend drinkers. A random sample of such accidents showed the following results:

Day / Sun / Mon / Tue / Wed / Thu / Fri / Sat / Total
Number / 38 / 24 / 25 / 28 / 29 / 60 / 56
Expected frequency

Test the claim that fatal DWI car crashes occur on the different days of the week with equal frequency. Take α = 0.05. What kind of Chi-Square test is this?

4. An ice cream supplier claims that among the four most popular flavors, customers have these preference rates: 62% prefer vanilla, 18% prefer chocolate, 12% prefer coffee, and 8% prefer walnut. A random sample of 200 customers produced the results in the table.

Flavor / Vanilla / Chocolate / Coffee / Walnut / Total
Number / 120 / 40 / 18 / 22
Expected frequency

Test the claim that the supplier has correctly identified customer preferences. Use α = 0.05.

What kind of Chi-Square test is this?

5. Among the drivers who had a car crash last year, a random sample of 88 is selected. The results categorized by age group are shown in the table.

Age / Under 25
(16%) / 25 – 44
(44%) / 45 – 64
(27%) / Over 64
(13%) / Total
Drivers / 36 / 21 / 12 / 19
Expected frequency

The number of drivers in each category is expected to be distributed as follows: 16%, 44%, 27%, and 13%. Test the claim the distribution of crashes conforms to the distribution of ages.
Use α = 0.05.

What kind of Chi-Square test is this?

6. A clothes manufacturer wants to know whether customers prefer any specific color over other colors in shirts. A random sample of 150 shirts is selected and the data are shown here. At α = 0.10, is there a color preference for the shirts?

Color / White / Blue / Black / Red / Yellow / Green
No. sold / 60 / 28 / 16 / 30 / 10 / 6

What kind of Chi-Square test is this?

7. A manager wants to know whether there is any preference in the flavors of popcorn sold during sporting events. A random sample of sales is selected and the data are shown below. Is there a flavor preference? Use α = 0.01.

Flavor / Plain / Barbecue / Butter / Cheese / Total
No. sold / 38 / 18 / 32 / 45

What kind of Chi-Square test is this?

8. A researcher wants to know if boys or girls prefer chocolate or vanilla ice cream. He collects a random sample of 400. The results are shown in the table.

Group / Prefer Chocolate / Prefer Vanilla / No preference / Total
Boys / 80 / 90 / 20
Girls / 70 / 110 / 30
Total

Test the claim of no preference at α = 0.05 level of significance. What kind of Chi-Square test is this?

9. A political scientists wishes to see whether a person’s political affiliation is related to his or her educational level. A random sample of 100 people is selected. The results are shown in the table. At α = 0.05, can the scientist conclude that political affiliation is dependent on the educational level? What kind of Chi-Square test is this?

Democrat / Republican / Independent / Total
No College / 20 / 18 / 9
Four-year degree / 8 / 15 / 9
Advanced degree / 6 / 7 / 8
Total

10. A sociologist wishes to determine whether there is a relationship between the sex of a person and the amount of alcohol consumed. A random sample of 100 people is selected and the following data are obtained.

Alcohol consumption / Total
Sex / Low / Moderate / High
Male / 25 / 18 / 20
Female / 8 / 19 / 10
Total

At α = 0.10, can the researcher conclude that alcohol consumption is related to sex?

What kind of Chi-Square test is this?

11. Suppose we want to investigate whether there is a relationship between real-estate salespersons’ standard of clothing and their success in their jobs. A random sample of 350 yielded the following results:

Success in the job
Below average / Average / Above average / Total
Poorly dressed / 19 / 17 / 6
Well dressed / 27 / 35 / 21
Very well dressed / 30 / 137 / 58
Total

At α = 0.01, can we conclude that there is a dependence between a real estate salesperson’ standard of clothing and success in the job?

What kind of Chi-Square test is this?

12. A new experimental drug was given to 120 patients, while 120 other patients received a placebo. After six months all the patients were evaluated and the results are shown in the following table:

Placebo / New drug / Total
Deteriorated / 6 / 11
Unchanged / 65 / 31
Improved / 49 / 78
Total

Using the level of significance α = 0.05, test whether the new drug is effective.

What kind of Chi-Square test is this?

13. It has been observed that in populations where lots of fish is consumed, incidence of prostate cancer among men is less. A study of 6272 men produced the following results concerning fish consumption and prostate cancer.

Prostate Cancer
Fish Consumption / No / Yes
Never/seldom / 110 / 14
Small part of diet / 2420 / 201
Moderate / 2769 / 209
Large part / 507 / 42

Perform a Chi-Square test to test the hypothesis that prostate cancer and fish consumption are independent. Use

What kind of Chi-Square test is this?

14. Most people have the impression that foreign made automobiles tend to be more reliable than US made cars. A survey asked consumers about problems they have had with their new cars in the first 12 months of ownership. The results are shown in the table:

Origin of vehicle
Asia / Europe / Us / Total
No problems / 88 / 79 / 83
Problems / 12 / 21 / 17
Total / 300

Test the hypothesis that the rate of problems is independent of the origin of the manufacturer. Use

What kind of Chi-Square test is this?

15. A lot of companies are outsourcing their IT and HR business segments. Below are the outsourcing data for two industry sectors:

Outsourcing Data
IT only / HR only / Both IT & HR
Financial / 1598 / 549 / 117
Industrial / 1269 / 412 / 99

Perform a Chi-square test to determine if there are significant differences between the companies in these two industry sectors with regard to their outsourcing. Use

What kind of Chi-Square test is this?