# Statistics of Manufacturing Exercise Bicycles

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A manufacturere of exercise bicycles is studying the relationship between the number of months an exercise bicycle has been owned and the length of time it was used last week. Data for a random sample of 7 owners are proviced in the table below.

Months owned (x) Hours used last week

14 6

8 8

5 7

3 9

10 6

4 8

12 7

a. Construct a scatter diagram for these data with "Months owned" on the horizontal (x) axis and "Hours used Last Week" on the vertical (y) axis.

Note: Try to make a relatively full use of the graph paper provided

b. Describe the general pattern of the relationship between the two variables.

c. Calculate the least squares regression line with hours used as the dependent variable and months owned as the independent variable.

Note: Express a and b to 4 decimal places of accuracy.

d. Plot the regression line on the scatter diagram you constructed in part (a)

Note: Show your calculations for x=4 and x=12.

e. Can it be concluded that the slope of the regression line is negative? Formulate and test the appropriate hypothesis at the 5% significance level. Use the critical value approach.

f. Construct a 95% confidence interval for B.

g. Interpret the numerical value of b in the sample regression line. What does it mean in the context of this question.

h. Use the equation of the regression line to predict hours used last week if an exericse bicycle has been owned for 11 months.

Note: Express your answer to 2 decmal places for accurancy.

(Please see attached file).

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