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statistical analysis

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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.
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1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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