Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Business Statistics (MGT223)

Exercises 4 –

Independent samples t-test, paired-test and tests of equality of variance

1. Two types of machine tool, each of equal cost, were being considered for use on a milling machine. Ten tools of each type were selected and their lifetime in hours was recorded.

a) Use SPSS to conduct an Independent samples t-test, stating and testing where possible any assumptions that you make.

b) Provide a brief summary of your findings for the production team.

2. Using the staffsurvey.sav data file, compare the mean satisfaction scores (totsatis) for permanent and casual staff (employstatus).

a. State and test where possible any assumptions that you make.

b. Interpret the output as fully as you can.  

c. Provide a non technical summary of your findings.

3. An educational test was conducted in two schools. The interest was not in the average score in each school, but the variance of the scores. The sample sizes were 20 and 18, and the sample variances 36 and 47 respectively. Regarding the samples as random samples from repeated tests in each school, do think that there is an underlying difference in the population variances?

Why is the qualifier at the beginning of the last sentence necessary? Why might an investigator of schools be as interested in differences in the variances as well as in differences in the means?

4. A company set up an experimental procedure to reduce the variability of the weight of a 'standard' weight of cement delivered to customer. Without the procedure, a sample of 10 deliveries gave a sample variance of 125kg, but with the experimental procedure the variance of a sample of 15 was reduced to 83kg. Is this good evidence that the procedure has worked?

5. A certain type of wood screw is sold in boxes described as 'average contents 100 screws'. In an attempt to reduce the variability of the number of screws in a box, a modification to the machine which filled the boxes was made. Sample boxes were taken before and after the modification, and the variances calculated. The sample sizes where both 50, and the before and after variances were 8.7 and 3.5. Do you think that the machine modification has been successful?

6. Extract from 2018-19 exam question

The number of visitors to a stately home were recorded for Saturday and Sunday over twenty weekends. Researchers were interested in whether visitor numbers were higher on Sundays. The data was analysed in IBM SPSS Statistics using a variety of tests and the resultant output is given at the end of this set of exercises.

a) Provide a full interpretation of these analyses, indicating the hypotheses that you are testing and the assumptions underpinning the tests.

b) Which of these tests is most appropriate? Explain your answer.

c) Write a paragraph summarising your findings, suitable for inclusion in a management report.

7. The data file EX4Q7.sav comprises observations that were taken on the output from a number of machines in the week before and the week after a special maintenance plan had been adopted.

a) Using an independent samples t test, examine the data to see if any improvements have taken place.  Check as far as you can any assumptions made.

b) Repeat the analysis using a Paired t test (assume that the outputs were recorded in the same order each time) you will need to create two new variables – Before and After), checking any assumptions that you make.

c) What conclusions do you come to?

SPSS Output for question 6