# statistical analysis

(See attached file for full problem description)

---

A. Circle the correct answer.

1. The null hypothesis is a claim about

a. the size of the sample.

b. the size of the population.

c. the value of a sample statistics.

d. the value of the population parameter.

2. when the null hypothesis is rejected, we conclude that

a. the alternate hypothesis is false also.

b. the alternate hypothesis is true.

c. the sample size is too large.

d. we used the wrong test statistic.

3. A Type II error is

a. rejecting Ha when it is true.

b. accepting a false Ho.

c. reject Ho when it is true.

d. not rejecting a false Ha.

4. In a test regarding a sample mean,  is not known. Under which of the following conditions can s be substituted for  and z used as the test statistic?

a. When n is 30 or more.

b. When n is less than 30.

c. When  is known.

5. Under what conditions would a test considered a one-tailed test.

a. When Ho contains  .

b. When there is more than one critical value.

c. When Ha contains = .

d. When Ha includes a < or > .

6. In a two sample test of means, n1 = 12 and n2 = 10. There are how many degrees of freedom in the test?

a. 22

b. 21

c. 20

d. none of the above

7. For tests of hypothesis for a single sample mean, a one-tailed test (rejecting region in the upper tail), using the 1% significance level, and with n=12, the critical value is:

a. 2.179

b. 2.681

c. 2.718

d. 3.106

8. The analysis of variance technique is a method for

a. comparing three or more means.

b. comparing F distribution.

c. measuring sampling error.

d. none of the above.

9. A treatment in ANOVA is

a. a normal population.

b. the explained population.

c. a source of variation.

d. the amount of random error.

10. A regression equation is used to

a. measure the association between two variables.

b. estimate the value of the dependent variables based on the independent variable.

c. estimate the value of the independent variable based on the dependent variable.

d. estimate the coefficient of correlation.

B. The mean length of a small counter balance bar is 43 millimeters. There is concern that the adjustments of the machine producing the bars have changed. Twelve bars (n=12) were selected at random and their lengths recorded. The lengths are 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42. Test the claim at the 0.02 level that there has been no change in the mean length.

C. Following is a partial ANOVA table:

Source SS df MS F

Stores .1370

Items 71.6131 8

Error 0.0221

Total 72.1037 26

Complete the table, and answer the following questions. Use the .05 significance level.

a. How many stores are there?

b. How many items are there?

c. What are the critical values of F for the stores and for the items?

d. Write out the null and alternate hypothesis for both stores and items.

e. what are your conclusions regarding both the stores and the items?

D. The following table shows the number of workdays absent based on the length of employment in years.

Number of Workdays Absent Y: 2 3 3 5 7 7 8

Length of Employment (in yrs) X: 5 6 9 4 2 2 0

Y X X*Y X2 Y2

2 5

3 6

3 9

5 4

7 2

7 2

8 0

Totals

Test at 5% level whether there is an association between the number of workdays absence and length of employment.

What is the linear regression equation? What is the estimated number of workdays absence when the worker has been on the job for 3 years?

E. A study is made by an auto insurance company to determine if there is a relationship between the driver's age and the number of automobile accident claims during a one-year period. From a sample of 300 claims, the following sample information was recorded.

Age (Years)

No. of Accidents Less than 25 25-50 Over 50 Total

0 37 101 74

1 16 15 28

2 or more 7 9 13

Total

Use the 0.05 significance level to find out if there is any relationship between the driver's age and the number of accidents.

---

(See attached file for full problem description)