Calculated value of the test statistic


1) A large city is in the process of voting on a bond issue to build a covered sports arena. A local political analyst wishes to determine if the level of income will impact on the decision of the voters. He takes a sample of 350 who plan to vote in the upcoming election.

                                                 Vote on Bond Issue

Income                                  Yes             No             Total
Under $20,000                         8               12               20
$20,000 — under $30,000        26              20               46
$30,000 — under $40,000       102              50              152
$40,000 — under $50,000        50               58              108
$50,000 or above                    14               10               24
Total                                     200              150             350

a) What is the appropriate table value for a test for independence at the 0.025 significance level?

b) What is the expected frequency of the $50,000 and over and No categories?

c) What is the calculated value of the test statistic?

2) The owner of a video store is interested in whether or not there is a difference in the proportions of VCR movies rented by members and non-members among movie titles. Three movies are selected and each person who rents them is identified as a member or non-member. A total of 350 people rent these movies and the responses are:

                                          Movie
Membership     Witness    Rambo    Karate Kid    Total
Member              21           14             70           105
Non-Member       79            86             80          245
'Total                 100          100           150          350

What are the degrees of freedom for the test of equal proportions?

What is the expected frequency of the cell Rambo and Non-member?

What is the computed value of the test statistic?

What is the critical value for a 0.01 significance level?

3) The following table shows the selling price and mileage of 7 used cars of a certain model.

mileage Price

22,600 $15,200

32,100 $12,500

43,800 $13,900

51,800 $9500

59,400 $11,600

65,500 $11,700

74,700 $8900

Identify the dependent and independent variable.

Find the least-squares regression line.

Using the least-squares regression line, predict the selling price of a car with 55,000 miles.

4) A statistics professor investigated some of the factors that affect an individual student's final grade in his course. He proposed the multiple regression model  where:

y = final mark (out of 100)

x1 = number of lectures skipped

x2 = number of late assignments

x3 = mid-term test mark (out of 100)

The professor recorded the data for 50 randomly selected students. The computer output is shown below.

187_Regression equation.jpg

Do these data provide enough evidence to conclude at the 5% significance level that the model is useful in predicting the final mark?

Test statistic = ____________________

Critical Value = ____________________

Conclusion: ____________________

Do these data provide enough evidence to conclude at the 5% significance level that the final mark and the number of skipped lectures are linearly related?

Test statistic = ____________________

Critical Value = ____________________

Conclusion: ____________________

Do these data provide enough evidence at the 5% significance level to conclude that the final mark and the number of late assignments are negatively linearly related?

Test statistic = ____________________

Critical Value = ____________________

Conclusion: ____________________

Do these data provide enough evidence at the 1% significance level to conclude that the final mark and the mid-term mark are positively linearly related?

Test statistic = ____________________

Critical Value = ____________________

Conclusion: ____________________

What is the coefficient of determination? What does this statistic tell you?

Interpret the coefficients b1 and b3.

b1 = ____________________

Interpretation: ____________

b3 = ____________________

Interpretation: __________

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Basic Statistics: Calculated value of the test statistic
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