Name: ___________________________________ ID: ______________________________
Introductory Statistics XXXXXXXXXXand Introductory Biostatistics XXXXXXXXXX
Assignment 3
Due date: Friday 18th October 2013 Assessment value: 9%
??If you collected data with a classmate, give this person’s name and ID number.
??You are expected to use Minitab for your analyses.
??Write your answers in the spaces provided.
??Your report should preferably be computer produced but there will be no penalty if it is neatly hand written.
Part A: Comparing 2 means [28 marks]
Plant scientists have developed a new variety of corn with increased amounts of the essential amino acid lysine. In a test of the protein quality of this corn and hence its ability to increase the weight of chickens, an experimental group of thirty 1-day-old male chicks were fed a ration containing the new corn. A control group of another thirty 1-day-old male chicks received a ration that was identical except that it contained normal corn. The weight gain in grams after a further 15 days was recorded. This data is in the file ChickWeights.xls
1. Complete the following table: [3 marks]
Group n Mean Standard deviation Standard error of the mean
Control
Experimental
2. Construct and attach a side-by-side boxplot comparing the control and experimental groups.
[1 mark]
3. Based on the summary statistics in 1. and your side-by-side boxplot in 2., comment on the
similarities and differences between the two groups. [3 marks]
4. a. Calculate and interpret a 95% confidence interval (CI) for the mean weight gain in grams after 15 days for the chickens fed the normal corn. [4 marks]
b. Calculate and interpret a 95% confidence interval (CI) for the mean weight gain in grams after 15 days for the chickens fed the experimental corn. [4 marks]
5. Use your CI’s in 4. to decide if there is a significant difference between the mean weight gain of these two groups. Justify your answer. [2 marks]
6. Hypothesis testing
a. State the null and the alternative hypotheses that test the question the plant scientists are
interested in. [2 marks]
b. State the assumptions you need to make about the population's distribution and the
selection of experimental units to test these hypotheses. [2 marks]
c. Use Minitab to calculate the test statistic and p-value for testing the hypotheses in 6a.
[2 marks]
Page 1 of 4
d. Explain whether you have evidence for or against the null hypothesis [1 mark]
e. State your conclusion from 6c. in a way that a non-statistician could understand. [1 mark]
7. The scientists were interested in whether the new corn variety improved the chicken's weight
gain, but to be commercially viable, the improvement needs to be greater than 5 grams. Based
on your results from question 6, what is your recommendation regarding the commercial
application of this new variety of corn? [2 marks]
8. This experiment was presented to a statistician who after critiquing it recommended that a
different experimental design should be use, one where each chick receives both the control
corn and new corn, so that the variability between chicks could be accounted for. What name is
given to this type of experimental design? [1 mark]
Part B(i): Analysing Proportions [16 marks]
Samples of flu viruses from infected people are sent for genotyping each year. The results are
reported to the World Health Organisation as part of their worldwide monitoring of influenza. The table below shows some of the genotypes found in New Zealand over the last four years.
Year
Genotype XXXXXXXXXX
A(H1N1)pdm XXXXXXXXXX
A(H XXXXXXXXXX
Influenza XXXXXXXXXX
Other XXXXXXXXXX
Total XXXXXXXXXX
1. What proportion of samples in 2009 were identified as A(H1N1)pdm09? [1 mark]
2. Construct and interpret a 95% confidence interval for the proportion in 1. [2 marks]
3. What proportion of samples in 2012 were identified as A(H1N1)pdm09? [1 mark]
4. Construct and interpret a 95% confidence interval for the proportion in 3. [2 marks]
5. Compare the confidence intervals from 2. and 4. Discuss the implications. [2 marks]
6. Hypothesis testing
a. Write down the null and alternative hypotheses for testing if the proportion of reported
cases of Influenza B has dropped significantly from 2011 to XXXXXXXXXXMake sure you define any symbols that you use) [2 marks]
b. Use Minitab to test the hypotheses in 6a. [2 marks]
c. Explain whether you have evidence for or against the null hypothesis [2 marks]
d. Write your conclusion from 6b. in a way that a non-statistician could understand. [2 marks]
Page 2 of 4
Part B(ii): Further analysis of traffic data [16 Marks]
In this section you will use the Analysis of traffic data to investigate the relationship
between your two categorical variables.
1. Construct a contingency table summarizing results for your two categorical variables.
[4 marks]
2. Construct an appropriate graph to display the data in your contingency table. [2 marks]
3. Discuss what your graph tells you about the relationship between your two categorical variables. [4 marks]
4. Contingency table analysis
a. Write down suitable null and alternative hypotheses for testing the relationship between
your two categorical variables using the contingency table. [1 mark]
b. Use MINITAB to test the hypotheses in 4a. [2 marks]
c. Explain whether you have evidence for or against the null hypothesis [1 mark]
d. Write your conclusion from 4b. in a way that a non-statistician could understand.
[2 marks]
NOTE: You will need to pay attention to possible problems caused by cells with small expected
counts.
Part C: Regression [30 Marks]
Data on 75 subjects are available from a respiration study at the Wellington Clinical School. The
measurements were taken with the subjects running at full speed on a treadmill (and can be regarded as a random sample from a population under study). Information on the following variables is in data file breath.xls:
MxO2 (maximum Oxygen absorbed, in litres per minute), Height (in cm),
MxHR (maximum heart rate, in beats per minute), Weight (in kg),
MxVn (maximum ventilation, in litres of air per minute), Age (in years),
MxCO2 (maximum Carbon Dioxide released, in litres per minute).
1. Conduct and attach a regression analysis, predicting MxO2 based on MxHR. (Minitab hint: Stat >Regression > Regression…)
a. Test if the slope is significantly different to zero by doing the following: [8 marks]
(i) State the null and alternative hypotheses in words and symbols.
(ii) State the test statistic and corresponding p-value for testing these hypotheses.
(iii) Explain whether you have evidence for or against the null hypothesis.
(iv) State your conclusion in a form that a non-statistician would understand.
Page 3 of 4
b. The R2 value [3 marks]
(i) State the R2 value.
(ii) Interpret this value in context.
(iii) Discuss whether this model would be useful for prediction.
c. Construct and attach a scatterplot of this data with the regression line on it. [1 mark]
d. Attach a copy of the residuals vs fits plot. [1 mark]
e. Use the residual plot to comment on whether the regression analysis is reasonable.
[2 marks]
2. Conduct and attach a regression analysis, predicting MxO2 based on MxVn.
(Minitab hint: Stat > Regression > Regression…).
a. The R2 value [3 marks]
(i) State the value.
(ii) Interpret this value in context.
(iii) Discuss whether this model would be useful for prediction.
b. Construct a scatterplot of this data with the regression line on it. [1 mark]
c. Attach a copy of the residuals vs fits plot. [1 mark]
d. Use the residual plot to comment on whether the regression analysis is reasonable.
[2 marks]
e. Construct by hand a 95% confidence interval for the slope in the regression equation
obtained in 2. [5 marks]
3. Predicting from the best model
a. Which variable, MxHR or MxVN, would give better predictions? Explain your decision.
[2 marks]
b. Use the regression model for the variable you chose in question 3a to predict the MxO2 for a subject (from the population of interest) with MxHR and MxVN values 175 and 120
respectively.
[1 mark]
++++++++