(a) Find the moment-generating function of the random variable X
having a chi-squared distribution with ν degrees of freedom. (10%)
(b) Use the moment-generating function in part (a) to find the mean and
variance of the chi-squared distribution with ν degrees of freedom.
(10%)
It is claimed that a new diet will reduce a person’s weight by 4.5 kilograms,
on average, in a period of 10 days. The following data table recorded the
weights of 10 men who followed this diet before and after a 10-day period.
Use the signed-rank test at the 0.05 level of significant to test the
hypothesis that the diet reduces the median weight by 4.5 kilograms
against the alternative hypothesis that the median difference in weight is
less than 4.5 kilograms. (Note: The critical values can be found in Table 1.)
(10%)
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