Q3.1

Many studies show that the likelihood of a single person experiencing poor health is reduced by pet ownership. Reasons for this could be many- including the need to exercise a dog, for example, which promotes health and over all general well being. Companionship associated with a pet is also likely to reduce stress thereby prompting a longer life.

University students decide to collect data on living alone grandparents (of friends and family).

They found that of the 361 living alone grandparents with at least one pet, 67 died within a 4 year period. Yet of those with no pet/s, 26 of the 89 in this group passed away within the 4 years.

Assuming the data has been collected randomly and is representative of the general population, answer the following:

a) Was this an experiment or an observational study? Explain. If it was an observational study was it retrospective or prospective? If it was an experiment how many treatments were there?

b) Is there evidence that those with a pet are significantly less likely to pass away than those with no pet? Write the appropriate hypotheses.

c) Test your hypothesis and state your conclusion. Use a = 0.025

d) Explain in context what your p-value means.

e) Create a 95% confidence interval for the difference in the death rate.

f) Interpret your interval in this context

[2+6+4+2+4+2 = 20 marks]

Q3.2

Aldi CANDYLAND bags of chocolate coated peanuts advertise they contain 200 grams. You purchase 10 bags and carefully weigh the contents and record the following weights (in grams): 201, 198, 206, 203, 197, 204, 203, 210, 208 and 205. The sample mean is 203.5 with standard deviation of 4.09 grams.

a) Use SPSS to create a 95% confidence interval for the true mean weight of all Aldi CANDYLAND chocolate coated peanuts.

b) Explain in context what the interval means.

c) Comment on the advertised pack label weight of 200 grams

d) Use SPSS to carry out a hypothesis test to see if there is evidence that the mean weight of bags is significantly different to the 200 grams on the label. Use a significance level of 5% and conclude in plain language.

[2+3+2+6 = 13 marks]

Q3.3

Are there differences in the number of demerit points men and women attain from driving offences? The following data was collected on the mean points held by a group of 31 men and 34 women.

Men Women

Count 31 34

Mean 9.8 6.2

Standard Deviation 2.9 1.8

a) Does it appear that men accumulate more demerit points on average than women drivers? Test and appropriate hypothesis and state your conclusion in plain language. (use a = 0.05)

b) Create a 90% confidence interval for the mean difference in demerit points between men and women. Interpret your interval in plain language.

[8+4 = 12 marks]

Q3.4

A sports psychologist believes he has a new positive motivation and training DVD which will vastly improve the capacity of a cricket player to bowl out the opposition. Each of 10 cricketers under go the training DVD with records firstly collected on how many successful “outs” they bowl BEFORE the DVD and then again AFTTER the DVD.

Each player bowled 2 overs with the total “outs” recoded below for the BEFORE training DVD and AFTER training DVD.

Player 1 2 3 4 5 6 7 8 9 10

Pre DVD outs 0 1 2 1 2 3 4 0 1 0

Post DVD outs 5 6 3 3 4 2 7 5 3 6

a) Is there evidence that the DVD helped bowlers play more effectively ie bowl out more batsmen? Carry out a hypothesis test (by hand or with SPSS) using a = 0.05 and write a conclusion.

b) Calculate a 90% confidence interval estimate for the average difference in the “outs” bowled. Based on your hypothesis test result, did you expect to find 0 in the interval? Explain.

[5+4 = 9 marks]

Q3. 5

Flu season is well known to be over winter and the colder months. A university student does not expect this to be the case in warmer climates such as Cairns in Queensland and so decides to see if there are significantly different counts of people being admitted to hospital with the flu. She gathers the data from hospital records and finds that 125 people were admitted over Spring, 95 over summer, 135 over autumn and 148 in winter.

a) If season has no bearing on the occurrence of the flu, how many people would you expect to see admitted to hospital in any one season?

b) To see if your results are unusual, will you perform a goodness-of-fit test or a test of independence?

c) State your hypotheses.

d) Check the conditions.

e) How many degrees of freedom are there?

f) Find x2 and the P-value.

g) State your conclusion.

[1+1+2+2+1+5+2 = 14 marks]

Q3.6 The following table shows data on randomly selected adults in the work force, on the use of internet and their education level.

Are internet usage and the education level independent?

Less than high school High School Tertiary

Used internet 200 921 1436

Did not use Internet 140 561 258

a) Write appropriate hypotheses.

b) How many degrees of freedom are there?

c) Find x2 and the P-value.

d) State your conclusion in plain language. Can you explain the reasons for your conclusion? (Hint compare your observed with your expected counts)

[2+1+5+4 = 12 marks]

Q3.7

Refer back to the question you tackled on time at table versus calories consumed for toddlers.

Does how long a toddler sits at the lunch table dictate the amount of calories they consume? To answer this question data was collected from a kindergarten on the number of minutes (time) toddlers sat at the table versus the amount of calories consumed, with the data saved in the file “lunchtime.sav” in moodle. (Note you will not need the data for the questions below.)

A regression analysis was undertaken with the output shown below.

Model Summary

Model R R Square Adjusted R

Square Std. Error of the

Estimate

1 .649a .421 .389 23.398

a. Predictors: (Constant), Time ANOVAa

Model Sum of Squares df Mean Square F Sig.

a. Dependent Variable: Calories

b. Predictors: (Constant), Time

Coefficients

Unstandardized Coefficients

B Std. Error

Standardized Coefficients

Beta

a. Dependent Variable: Calories

a) Give the regression equation.

b) Interpret the slope

c) State the appropriate hypothesis for the slope.

d) Test your hypothesis and state your conclusion in plain language.

e) What further plots should be produced in SPSS to check this model is valid? [2+3+4+4+2 = 15 marks]

Many studies show that the likelihood of a single person experiencing poor health is reduced by pet ownership. Reasons for this could be many- including the need to exercise a dog, for example, which promotes health and over all general well being. Companionship associated with a pet is also likely to reduce stress thereby prompting a longer life.

University students decide to collect data on living alone grandparents (of friends and family).

They found that of the 361 living alone grandparents with at least one pet, 67 died within a 4 year period. Yet of those with no pet/s, 26 of the 89 in this group passed away within the 4 years.

Assuming the data has been collected randomly and is representative of the general population, answer the following:

a) Was this an experiment or an observational study? Explain. If it was an observational study was it retrospective or prospective? If it was an experiment how many treatments were there?

b) Is there evidence that those with a pet are significantly less likely to pass away than those with no pet? Write the appropriate hypotheses.

c) Test your hypothesis and state your conclusion. Use a = 0.025

d) Explain in context what your p-value means.

e) Create a 95% confidence interval for the difference in the death rate.

f) Interpret your interval in this context

[2+6+4+2+4+2 = 20 marks]

Q3.2

Aldi CANDYLAND bags of chocolate coated peanuts advertise they contain 200 grams. You purchase 10 bags and carefully weigh the contents and record the following weights (in grams): 201, 198, 206, 203, 197, 204, 203, 210, 208 and 205. The sample mean is 203.5 with standard deviation of 4.09 grams.

a) Use SPSS to create a 95% confidence interval for the true mean weight of all Aldi CANDYLAND chocolate coated peanuts.

b) Explain in context what the interval means.

c) Comment on the advertised pack label weight of 200 grams

d) Use SPSS to carry out a hypothesis test to see if there is evidence that the mean weight of bags is significantly different to the 200 grams on the label. Use a significance level of 5% and conclude in plain language.

[2+3+2+6 = 13 marks]

Q3.3

Are there differences in the number of demerit points men and women attain from driving offences? The following data was collected on the mean points held by a group of 31 men and 34 women.

Men Women

Count 31 34

Mean 9.8 6.2

Standard Deviation 2.9 1.8

a) Does it appear that men accumulate more demerit points on average than women drivers? Test and appropriate hypothesis and state your conclusion in plain language. (use a = 0.05)

b) Create a 90% confidence interval for the mean difference in demerit points between men and women. Interpret your interval in plain language.

[8+4 = 12 marks]

Q3.4

A sports psychologist believes he has a new positive motivation and training DVD which will vastly improve the capacity of a cricket player to bowl out the opposition. Each of 10 cricketers under go the training DVD with records firstly collected on how many successful “outs” they bowl BEFORE the DVD and then again AFTTER the DVD.

Each player bowled 2 overs with the total “outs” recoded below for the BEFORE training DVD and AFTER training DVD.

Player 1 2 3 4 5 6 7 8 9 10

Pre DVD outs 0 1 2 1 2 3 4 0 1 0

Post DVD outs 5 6 3 3 4 2 7 5 3 6

a) Is there evidence that the DVD helped bowlers play more effectively ie bowl out more batsmen? Carry out a hypothesis test (by hand or with SPSS) using a = 0.05 and write a conclusion.

b) Calculate a 90% confidence interval estimate for the average difference in the “outs” bowled. Based on your hypothesis test result, did you expect to find 0 in the interval? Explain.

[5+4 = 9 marks]

Q3. 5

Flu season is well known to be over winter and the colder months. A university student does not expect this to be the case in warmer climates such as Cairns in Queensland and so decides to see if there are significantly different counts of people being admitted to hospital with the flu. She gathers the data from hospital records and finds that 125 people were admitted over Spring, 95 over summer, 135 over autumn and 148 in winter.

a) If season has no bearing on the occurrence of the flu, how many people would you expect to see admitted to hospital in any one season?

b) To see if your results are unusual, will you perform a goodness-of-fit test or a test of independence?

c) State your hypotheses.

d) Check the conditions.

e) How many degrees of freedom are there?

f) Find x2 and the P-value.

g) State your conclusion.

[1+1+2+2+1+5+2 = 14 marks]

Q3.6 The following table shows data on randomly selected adults in the work force, on the use of internet and their education level.

Are internet usage and the education level independent?

Less than high school High School Tertiary

Used internet 200 921 1436

Did not use Internet 140 561 258

a) Write appropriate hypotheses.

b) How many degrees of freedom are there?

c) Find x2 and the P-value.

d) State your conclusion in plain language. Can you explain the reasons for your conclusion? (Hint compare your observed with your expected counts)

[2+1+5+4 = 12 marks]

Q3.7

Refer back to the question you tackled on time at table versus calories consumed for toddlers.

Does how long a toddler sits at the lunch table dictate the amount of calories they consume? To answer this question data was collected from a kindergarten on the number of minutes (time) toddlers sat at the table versus the amount of calories consumed, with the data saved in the file “lunchtime.sav” in moodle. (Note you will not need the data for the questions below.)

A regression analysis was undertaken with the output shown below.

Model Summary

Model R R Square Adjusted R

Square Std. Error of the

Estimate

1 .649a .421 .389 23.398

a. Predictors: (Constant), Time ANOVAa

Model Sum of Squares df Mean Square F Sig.

a. Dependent Variable: Calories

b. Predictors: (Constant), Time

Coefficients

Unstandardized Coefficients

B Std. Error

Standardized Coefficients

Beta

a. Dependent Variable: Calories

a) Give the regression equation.

b) Interpret the slope

c) State the appropriate hypothesis for the slope.

d) Test your hypothesis and state your conclusion in plain language.

e) What further plots should be produced in SPSS to check this model is valid? [2+3+4+4+2 = 15 marks]

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