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hypothesis testing

1) A hypothesis test is to be carried out to see whether or not there is evidence to suggest
that 20-year-old female undergraduates are signicantly taller than their 18-year-old
counterparts (who have mean height 161.24 cm). Let X be the random variable
representing the height of a randomly-chosen 20-year-old female undergraduate. The
variance of X is unknown.
(i) In order to carry out the test, the heights of ten randomly-chosen 20-year-old female
undergraduates are obtained. State an assumption that must be made about the
distribution of X if we are to carry out the test using the t distribution. [5%]
(ii) How many degrees of freedom will the t distribution have in this case?
I dont know where to start

Reply 1

username236426

Original post by sammy3000

(i) To compare two samples with the t test, both samples must be normally distributed and independent with variance unknown.

(ii) This depends on whether you're pooling (collecting) the variances or not. If the sample size of group 1 and group 2 is n1 and n2 respectively then the degrees of freedom is:

- (unpooled) the smaller of n1 - 1 and n2 - 1.
- (pooled) n1 + n2 - 2.