# BUSINESS STUDIES

**Do men tend to marry women who are younger than themselves?**

**We can use the information about age of mother and age of father to address this question. Produce a paired samples t-test using these two variables.**

In your sample what is the average difference in age between mothers and fathers? SPSS may give a positive or a negative difference. Remove any negative sign before entering the answer. (Give your answer correct to two decimal places.)

Mean (difference) =

1 points

**Question 2**

What is the standard deviation of the difference scores? (Give your answer correct to two decimal places.)

*s _{d} *=

1 points

**Question 3**

Give the value of the *t* statistic (Note: possible answers for *t* may be positive or negative. Remove any negative sign before entering the answer. Give your answer correct to two decimal places.)

*t* =

**Question 4**

The degrees of freedom is

*df* =

1 points

**Question 5**

The p-value for this test should be reported as:

p < 0.05 | ||

p > 0.05 | ||

p = 0.001 | ||

p < 0.001 | ||

p = 0.000 | ||

p > 0.001 |

1 points

**Question 6**

Select one of the following statements:

The p-value is less than 0.050 | ||

The p-value is equal to 0.050 | ||

The p-value is greater than 0.050 |

1 points

**Question 7**

Is the following statement true or false?

The t-test shows a significant difference between the means.

True

False

2 points

**Question 8**

What can we conclude from this paired samples *t*-test?

Select one of the following statements:

In the population, men on average marry women who are older than themselves. | ||

In the population, men on average marry women who are the same age as themselves. | ||

In the population, on average, men marry women who are younger than themselves. | ||

We can’t draw any conclusion about whether men on average marry younger or older women |

2 points

**Question 9**

Complete the following sentence, giving the answers correct to 2 decimal places.

We can be 95% confident that on average men marry women who are between Blank 1 years and Blank 2 years younger than themselves.

2 points

**Question 10**

The Australian National Health Organisation conducted a study to investigate whether a physiotherapy program reduces pain in people with chronic shoulder pain. A sample of 67 people with chronic shoulder pain undertook 10 weeks of physiotherapy treatment. The level of pain was recorded before the physiotherapy program commenced, and again at the end of the 10 week program. A paired samples t-test was conducted on the data. Using the attached SPSS output, complete the following report.

It was hypothesised that a 10 week physiotherapy program would reduce the level of pain in people suffering from chronic shoulder pain.

In a random sample of Term 1 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 people suffering from chronic shoulder pain, on average the pain level after the physiotherapy program was Term 2 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 ( = Term 3 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 , *s* = Term 4 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 ) than before the program ( = 5.79, *s* = 1.58). A paired samples t-test shows that this difference in mean pain level ( * _{d}* = Term 5 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 ,

*s*Term 6 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 ) is Term 7 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 ,

_{d}=*t*(Term 8 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 )= Term 9 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 ,

*p*= Term 10 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 . The 95% confidence interval indicates that the mean pain level is between 0.21 and Term 11 lower higher significant not significant 5.15 67 1.29 0.16 0.27 0.026 0.64 1.75 0.21 1.07 2.99 66 0.004 0.002 lower after the physiotherapy program.

As expected, the physiotherapy program reduces the level of pain in people with chronic shoulder pain.

4 points

** **

**Question 11**

A large retail chain are concerned about the number of customer complaints they receive about their staff. They engage a personnel consultant to train their staff in customer relations. They randomly selected 80 staff and recorded how many complaints each member of staff had received in the previous week. In the week after the training program was completed, the number of complaints was again recorded. It was hypothesised the number of complaints would be lower after the training program. Use the drop down menus to complete the following report:

It was hypothesised that the number of customer complaints made against staff in a large retail chain would be lower after a training program was introduced.

In a random sample of 80 staff, on average the number of complaints in the week after the training program was Term 1 lower higher significant not significant sufficient insufficient 27.60 26.74 0.57 0.39 0.86 5.63 1.37 2.12 0.001 0.327 0.174 0.087 ( = Term 2 lower higher significant not significant sufficient insufficient 27.60 26.74 0.57 0.39 0.86 5.63 1.37 2.12 0.001 0.327 0.174 0.087 , *s* = 7.05 ) than before the program ( = 27.60, *s* = 5.14. A paired samples t-test shows that this difference in mean number of complaints ( * _{d}* = Term 3 lower higher significant not significant sufficient insufficient 27.60 26.74 0.57 0.39 0.86 5.63 1.37 2.12 0.001 0.327 0.174 0.087 ,

*s*Term 4 lower higher significant not significant sufficient insufficient 27.60 26.74 0.57 0.39 0.86 5.63 1.37 2.12 0.001 0.327 0.174 0.087 ) is Term 5 lower higher significant not significant sufficient insufficient 27.60 26.74 0.57 0.39 0.86 5.63 1.37 2.12 0.001 0.327 0.174 0.087 ,

_{d}=*t*(79)= Term 6 lower higher significant not significant sufficient insufficient 27.60 26.74 0.57 0.39 0.86 5.63 1.37 2.12 0.001 0.327 0.174 0.087 ,

*p*= Term 7 lower higher significant not significant sufficient insufficient 27.60 26.74 0.57 0.39 0.86 5.63 1.37 2.12 0.001 0.327 0.174 0.087 . The 95% confidence interval indicates that on average the number of complaints is between Term 8 lower higher significant not significant sufficient insufficient 27.60 26.74 0.57 0.39 0.86 5.63 1.37 2.12 0.001 0.327 0.174 0.087 less and Term 9 lower higher significant not significant sufficient insufficient 27.60 26.74 0.57 0.39 0.86 5.63 1.37 2.12 0.001 0.327 0.174 0.087 more after the training program.

There is Term 10 lower higher significant not significant sufficient insufficient 27.60 26.74 0.57 0.39 0.86 5.63 1.37 2.12 0.001 0.327 0.174 0.087 evidence to suggest that the training reduces the number of complaints.

4 points