Statistics Assignment Questions

Q1 Consider again the situation described in Assignment  Question 5: from a random sample of 60 motorists during a particular week, 9 had purchased diesel.

The owner wants to test whether this gives evidence to contradict his belief that 10% of customers use diesel.

 

(a) State, in words and in symbols, the hypotheses to be tested. [2]

(b) What is the p-value? [1]

(c) Is there evidence to reject the null hypothesis? Justify your answer. [1]

 

(d) State the conclusion in context. [2]

 

(e) Compare this analysis to that of Assignment 2 Question 5(c). Discuss. [2]    
 
Q2 Consider again the data file NZ exports 2013 and 2014.xlsx. Suppose we want to carry out a formal hypothesis test of whether the value of NZ exports to these countries has increased from 2013 to 2014.

 

(a) State, in words and in symbols, the hypotheses being tested. [3] 

  
(b) State the appropriate p-value.  [1]

(c) Is there evidence to reject the null hypothesis? Justify your answer. [1]

 

(d) State the conclusion in context. [2]

 

(e) Examine an appropriate normal probability plots. What does it suggest? [3]

Q3 Consider again the situation described in Assignment 2 Question 1. Suppose we want to carry out a formal test of whether Loyalty is related to Length of Service.

 

(a) State the hypotheses to be tested.    [2]

(b) Calculate the expected frequencies.    [1]

(c) What is the p-value? [1]

(d) State the conclusion in context, justifying your answer. [2]

 

(e) Calculate the proportion who would leave for each age group. What does it suggest?    [2]

 
Q4 The manager of the purchasing department of a large organization wants to develop a model for predicting the time it takes to process invoices. Data are collected for 30 days, giving the number of invoices completed and the time taken (in hours). The data are in the file INVOICES.xls.

 

(a) Construct an appropriate scatterplot. [2]

(b) Describe what the scatterplot in (a) suggests about the relationship between number of invoices and time taken.    [2]

(c) Use Excel to find the least squares regression line for predicting Time based on Invoices Completed.    [1]

(d) Interpret, in context, the slope coefficient in the model.    [1]

(e) Give the value, and interpret the meaning, of the R Square.    [2]

(Contd overleaf)
 
(Q4 contd)

 

(f) Give the value, and interpret the meaning, of the Standard Error ( ).    [2]

(g) Predict the time taken to process 150 invoices.    [2]

(h) Construct a residual plot of the residuals against the fitted values. Comment on what it shows.    [2]

(i)How strong is the evidence for a relationship between Time and Invoices Completed ?    [1]

 

Q5 Extension Question  this is not compulsory, and carries no extra marks this time. But it is an opportunity to test your knowledge against  a more challenging question. 

 

Refer back to the data in the file NZ exports 2013 and 2014.xlsx. Use regression analysis to address the question of whether the value of NZ exports to these countries has increased from 2013 to 2014. Discuss the main differences between this and the approach taken in Question 2 of this assignment. Which seems more appropriate?