Question 5 A study was undertaken to investigate a new method of measuring body

Question

Question 5
A study was undertaken to investigate a new method of measuring body fat composition. The MINITAB worksheet bodyfat.mtw contains the variables age, giving the age (in years), and bodyfat, giving the body fat (in %), for each of fourteen women.

A standard method of measuring body fat gives a mean measurement of 29% for these
women, and it is of interest to see whether this new method of measuring body fat composition differs from the standard. It can be assumed that the data for measuring body
fat can be modelled using a normal distribution whose mean and standard deviation are not
known.

(a) In this part you are asked to carry out a fixed-level test, using a 5% significance level, of the null hypothesis H0 : µ = 29, where µ is the population mean measurement of body
fat composition with the new method.
• Write down the alternative hypothesis.
• State the test statistic and write down its null distribution.
• Obtain the rejection region of the test statistic.
• Write down the observed value of the test statistic. (You should use MINITAB to
obtain this value.) [7]

(b) State your conclusions from the test.5

Explanation / Answer

H0: mu =29

Ha: mu not equals 29

Two tailed test

---------------------

n = 14

df =13

As n <30, t test is used here

since p<0.05 reject null hypothesis

The two means are different

31.4 25.9 25.2 31.1 34.7 42 29.1 32.5 30.3 33 33.8 41.1 34.5 Mean 32.32143 Std dev 4.89995 Std error 1.359001 t 23.78322 p <0.0001

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