MAS1401 Practical Exercises 3. [Assessed!]
Hand in your solutions at the Maths and Statistics General Office on
the 5th floor of Merz Court by 4pm on Thursday 15th March.
As usual, the data for the questions below can be found at:
http://www.mas.ncl.ac.uk/~ndw/mas1401.htm
1. This question uses the Minitab worksheet called Haematocrit which you used
in Practical 2. Open this worksheet.
a) Give a numerical estimate (a single number) of the population mean female
haematocrit level. Write this in your solutions. [4 Marks]
b) Use the Minitab option Stat > Basic Statistics > 1-sample t… to construct
a 95% Confidence Interval for the population mean female haematocrit level.
Write this interval into your solutions. [4 Marks]
c) Construct a 99% Confidence Interval for the population mean female
haematocrit level. Write this interval into your solutions. Note that you will
need to use the “Options…” button in the dialogue box to change the
confidence level. [4 Marks]
d) Construct a 99.9% Confidence Interval for the population mean female
haematocrit level. Write this interval into your solutions. [4 Marks]
e) In your solutions, say what happens to the Confidence Interval for the
population mean as you increase your level of confidence. [4 Marks]
f) Now construct a 99.9% Confidence Interval for the population mean male
haematocrit level. Write this interval into your solutions. [4 Marks]
g) In your solutions, compare the 99.9% Confidence Intervals for females and
males, saying what you think this tells you about how the true population
mean haematocrit level for women compares to the true population mean
haematocrit level for men. [6 Marks]
2. This question concerns the class data on shoe sizes, which are stored in the
Minitab worksheet called Class Shoe Sizes on the web-site. Open this
worksheet.
a) Use Minitab to construct a 95% Confidence Interval for the female
population mean shoe size. Write this interval in your solutions. [4 Marks]
b) Use Minitab to construct a 95% Confidence Interval for the male
population mean shoe size. Write this interval in your solutions. [4 Marks]
c) A shoe retailer believes the average foot size for young women in the UK is
6.0. Carry out an appropriate hypothesis test to investigate whether there is
evidence that the population from which the class data is drawn has a different
mean from this. In your solutions, you should quote the p-value, and interpret
this in terms of how strong is the evidence you have against the null
hypothesis. If the null hypothesis appears to be false, say in your solutions
how the population mean from which the class data is drawn appears to differ
from the null hypothesis. [6 Marks]
d) The same retailer believes the average foot size for young men in the UK is
9.0. Carry out an appropriate hypothesis test to investigate whether there is
evidence that the population from which the class data is drawn has a different
mean from this. In your solutions, you should quote the p-value, and interpret
this in terms of the how strong is the evidence you have against the null
hypothesis. If the null hypothesis appears to be false, say in your solutions
how the population mean from which the class data is drawn appears to differ
from the null hypothesis. [6 Marks]
3. This question uses the Haematocrit data again, so re-open that work-sheet.
a) We are interested in the population mean difference, that is:
Female Population Mean Haem. – Male Population Mean Haem.
Calculate an estimate (a single number) for this quantity, and write this in
your solutions. [4 Marks]
b) Use the Minitab option Stat > Basic Statistics > 2-sample t… to construct
a 95% Confidence Interval for the population mean difference. Note you
should tick “Assume equal variances” in the dialogue box! Write this
confidence interval in your solutions. [4 Marks]
c) Looking at the confidence interval you gave in part b), do you think it
would be reasonable to suggest that the population mean haematocrit for
females and males is the same? Give your answer, with justification, in
your solutions. [4 Marks]
d) If you look at the Minitab output you obtained in part b), you will see there
is a p-value. This is in fact the result of a 2-sample t-test of the null
hypothesis:
H0: the population mean haematocrit is equal for males and females,
against the alternative hypothesis:
HA: the population mean haematocrit for males and females differs.
In your solutions, interpret the result of this hypothesis test, saying
whether or not it supports the conclusion you obtained in part c). [6 Marks]
4. This question uses Data Set 2 in your own personalized collection:
a) Use Minitab to construct a 95% Confidence Interval for the population mean
difference in crop yields:
Fertilizer A mean yield – Fertilizer B mean yield
and write this confidence interval in your solutions. [4 Marks]
b) Use Minitab to test the hypothesis that the mean yields for Fertilizer A and
Fertilizer B are in fact the same. Write the results for this hypothesis test in
your solutions. [4 Marks]
c) State your conclusions concerning the relative performances of Fertilizer A
and Fertilizer B, in non-statistical terms, in your solutions. [4 Marks]
TOTAL: 80 MARKS
Hand in your solutions at the Maths and Statistics General Office on
the 5th floor of Merz Court by 4pm on Thursday 15th March.