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In: Statistics and Probability

A student hourly employee does small secretarial projects. Her manager wants to learn about the relationship...

A student hourly employee does small secretarial projects. Her manager wants to learn about the relationship between the number of projects (y) the student completes in a day and the number of hours (x) she works in a day. A random sample of nine days provided the following information:

Working Hours # of projects
1 2
2 3
3 5
4 6
4 5
6 8
7 9
7 8
8 10

a) Define variable types [Choose all that applies]:

Working hours (X): response, predictor, dependent, independent

Number of Projects (Y): response, predictor, dependent, independent

b) Sketch scatter plot for the number working hours and the number of projects.

c) Does the scatter plot in part b) reveal a linear the number of projects and the number of working hours? Explain.

d) Calculate and verify b0 and b1 in the provided output, write out the estimated SLM of the number of projects as a linear function of the working hours.

Coefficients Standard error
Intercept 1.1018 .3777
Working hours 1.0972 .0725

e) Using the estimated SLM, predict the number of projects completed in 5 hours.

f) Formally, test if there is a linear relationship between the number of projects and the number of working hours. Use α = 0.05.

i. State H0 and Ha.

ii. Calculate the test statistic.

iii. Make decision using the p-value approach.

iv. Draw conclusion.

g) Compute the 95% confidence interval for the regression slope.

h) Do the values in the 95% confidence interval support the existence of significant positive linear relationship between the number of projects and the number of working hours? Explain.

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Expert Solution

orchestra answered 2 years ago
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