Statistics

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Instructions:

  1. Type your answers directly into this document.
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  7. This Assignment is worth 12% of your total grade for STAT170. You may discuss the Assignment with your classmates if you wish, but must then complete all of the calculations and writing by yourself. Note: every semester, several students receive a mark of 0 for this Assignment, due to plagiarism. Ensure that you do not copy parts of your friends’ Assignment submissions. Submitting your assignment via iLearn is a declaration that the work is your own.

Information:

 

This assignment is worth 12% and is marked out of 50. Penalties apply as follows:

 

Submitted on Wednesday after 5pm:   Deduct 15 marks

Submitted on Thursday:                     Deduct 20 marks

Submitted on Friday:                                              Deduct 35 marks

 

 

 

Q1 Q2 Q3 Q4 Total
 

 

 

       
10 13 10 17 50

 

 

 


Question 1   (10 marks)

 

Include an appropriate diagram for each part of this question. You can sketch these diagrams and paste in a photo of your sketch, along with your solutions.

 

  1. BranCrunch is a new breakfast cereal. Boxes of BranCrunch are labelled ‘ 675 grams’ but there is some variation. The actual mean weight is 675 grams with a standard deviation of 21 grams.
    1. Dan’s Discount Store sells BranCrunch in mega-packs of 8 boxes. Assuming the weights of boxes of BranCrunch are normally distributed, find the probability that the average weight of a mega-pack of BranCrunch is higher than 665 grams.

 

 

 

 

 

 

 

 

 

 

  1. Louie’s Convenience Store receives a shipment of 30 boxes of BranCrunch. Louie’s will complain to the manufacturers if the total weight of this shipment is lower than 20 kg. Find the probability that Louie’s Convenience Store will complain about the shipment and explain why the information about the weights of BranCrunch following a normal distribution is not necessary to answer this part of the question.

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. In 2014 the Department of Social Services reported that 32% of current marriages in Australia were expected to end in divorce.

Find the probability that more than 8 marriages out of a random sample of 20 marriages which were current in 2014 would end in divorce.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

Question 2 (13 marks)

Lean body mass is the amount of weight carried on the body that is not fat. Metabolic rate is the rate at which the body consumes energy. The following Minitab output was constructed using data recorded in a fitness study which was designed to compare the lean body masses and also the metabolic rates of adolescent males and adolescent females. Use this output to answer the questions which follow.

 

Two-sample T for LeanBodyMass

 

Sex      N   Mean  StDev  SE Mean

Male    75  52.63   6.66     0.77

Female  75  43.42   6.05     0.70

 

Difference = μ (Male) – μ (Female)

Estimate for difference:  9.21

95% CI for difference:  (****, ****)

T-Test of difference = 0 (vs ≠): T-Value = ****  P-Value = ****  DF = ****

Both use Pooled StDev = 6.3633

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Two-sample T for MetRate

SE

Sex      N  Mean  StDev  Mean

Male    75  1626    227    26

Female  75  1258    172    20

 

Difference = μ (Male) – μ (Female)

Estimate for difference:  367.9

95% CI for difference:  (****, ****)

T-Test of difference = 0 (vs ≠): T-Value = ****  P-Value = ****  DF = ****

Both use Pooled StDev = 201.5088

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Explain why you could not use paired t-tests for these comparisons:
    Question 2 continued

 

Research Question:  Is there a difference between the average lean body mass of adolescent males and adolescent females?

 

 

 

  1. Calculate a 95% confidence interval to estimate the difference between the average lean body mass of adolescent males and the lean body mass of adolescent females. You should comment on the validity of any underlying assumptions.

 

 

 

 

 

 

 

  1. Use this interval to comment on the research question above.

 

 

 

 

 

Research Question:  Is there a difference between the average metabolic rate of adolescent males and adolescent females?

 

 

 

Metabolic rate is the rate at which the body consumes energy. It is an important variable in studies of weight gain, exercise and health.  Use an appropriate hypothesis test to answer this research question.

 

Hypothesis Test:

 

 

 

 


 

Question 3 (10 marks)

20 females took part in a three week exercise programme called “Get In Shape”. As part of an evaluation of the “Get In Shape” programme, weights for each of these 20 females were measured both at the beginning and at the end of the programme. The output below was produced from the results of this evaluation. Use the most appropriate part/s of this output to answer the questions which follow.

 

Two-Sample T-Test and CI: WeightBeginning, WeightEnd

 

Two-sample T for WeightBeginning vs WeightEnd

 

N   Mean  StDev  SE Mean

WeightBeginning  20  64.74   5.99      1.3

WeightEnd        20  62.61   6.56      1.5

 

 

Difference = μ (WeightBeginning) – μ (WeightEnd)

Estimate for difference:  2.13

95% CI for difference:  (-1.89, 6.15)

T-Test of difference = 0 (vs ≠): T-Value = 1.07  P-Value = 0.290  DF = 38

Both use Pooled StDev = 6.2809

 

 

Paired T-Test and CI: WeightBeginning, WeightEnd

 

Paired T for WeightBeginning – WeightEnd

 

N   Mean  StDev  SE Mean

WeightBeginning  20  64.74   5.99     1.34

WeightEnd        20  62.61   6.56     1.47

Difference       20  2.133  2.260    0.505

 

 

95% CI for mean difference: (1.075, 3.191)

T-Test of mean difference = 0 (vs ≠ 0): T-Value = 4.22  P-Value = 0.000

 

 

 


 

 

Question 3 continued

 

 

Statement True or False?
One of the females who took part in the Get in Shape programme lost over 6 kilograms  
Weights were a little more variable at the beginning of the Get in Shape programme than at the end of the programme.  
All of the females who took part in the Get in Shape programme lost some weight.  

 

 

 

 

 

 

 

 

 

 

 

 

 

Research Question: On average, do adolescent females who take part in the “Get in Shape” programme experience a significant change in their body weights?

 

 

 

 

 

Using the appropriate part/s of the output on the previous page, carry out a hypothesis test to answer this research question.    

 

Hypothesis Test:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

Question 4 (17 marks)

The Energy study was conducted over a six year period to investigate factors which could be used to predict the net hourly energy output of a power plant. The Minitab file, Energy.mtw, which is on iLearn consists of a randomly selected sample of 100 observations recorded during the course of the study. Each observation consists of information recorded on the following variables.

Variable                    Description

AirTemp                                            Hourly average air temperature (°C)

Energy                                               Net hourly electrical energy output (megawatts)

 

Research Question: Is air temperature a useful predictor of energy output?

 

 

 

 

  1. Use the Minitab file, mtw, to fit a linear regression model for predicting energy output from air temperature. Cut and paste the following output into the space below:
    1. Appropriate Minitab plots for checking each of the three assumptions of a linear model. Do not use the ‘four in one’ graph option in Minitab. Comments on each of these assumptions should go into your report on the following page.
    2. The regression analysis of Energy vs AirTemp from Minitab

 

 

 

 


 

Question 4 continued

 

  1. Write a short statistical report on the regression analysis from part a.

 

Introduction:

 

 

 

 

 

 

 

 

 

                Methods:

 

 

 

 

 

 

 

 

 

 

 

 

                Results:

 

 

 

 

 

 

 

 

 

 

 

                Conclusion:

 

 

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