A Meteorologist observes weekly rainfall and records this data in the Rainfall dataset.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Question 1 (Regression)

A researcher wants to study the relationship between the dosage of a medicine and the average response as measured on a sample of patients. The researcher collects data on the dosage and the response and records them in Minitab.

You are provided with a dataset called MedicineResponseData on Canvas, which contains the following data:

Worksheet column	Description
Response	The average response of the sample of patients
Dosage	The dosage of medicine used

 

(a)    Construct a scatterplot of the data and comment on the relationship between Dosage and Response.

(b)   Calculate the correlation coefficient and interpret it.

(c)    Fit a model of the form , report the fitted model and interpret the value of .

(d)   Calculate a 95% confidence interval for the  coefficient.

(e)    Test the hypothesis at the 5% level of significance:

H0:

HA:

What do the results of the hypothesis test imply for the regression model?

(f)    Report and interpret the coefficient of determination.

(g)   Plot the regression line onto a scatterplot of the data and plot a 95% prediction band.

(h)   Plot a histogram of the residuals and comment on its shape.

(i)     Report whether the assumptions of linear regression are satisfied. 

Question 2 (Basic Stats and ANOVA)

A teacher wants to compare the performance of 4 classes in a certain year group. There are 6 students in each class group, and each took the same exam which was marked by the teacher. This data is recorded in the Marks_by_Class dataset on Canvas.

Worksheet column	Description
Class	The Class Group: A, B, C, D
Mark	The Mark obtained by the student in the test

           

(a)    Produce summary statistics for Mark by Class and interpret your findings.

(b)   Carry out a one-way ANOVA on the data to determine whether the Marks differ by Class Group. 

Question 3 (Graphs and Hypothesis Tests)

A Meteorologist observes weekly rainfall and records this data in the Rainfall dataset.

Worksheet column	Description
Rainfall	The rainfall each week in cm

The historical weekly rainfall has been Normally Distributed with a mean of 100.

(a)    Verify that the rainfall data is Normally Distributed.

(b)   Carry out a hypothesis test of the rainfall values against the historical average rainfall at the 5% level of significance.

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