Question

3. A study is being done to compare the effectiveness of two techniques of performing a high jump. A group of 35 participants each performed the high jump twice, once using each of the two techniques, and the height of their jumps was recorded.

a) State a parameter of interest (i.e. a parameter you want to test/estimate).
b) Should this be a one-sided or two-sided test?
c) State the null hypothesis and alternative hypothesis.
d) Describe how you would set up a randomized experiment using coins, dice, cards etc. if

you had the actual data set.
e) Suppose the average difference in height between method one and method two is 2.6

cm and the standard deviation of the differences in height is 8.1 cm. Use appropriate formulas to compute a standardized statistic assuming the null hypothesis and determine the strength of evidence. Compute a 95% confidence interval using the 2SD method.

Answer 1

a)The parameter of interest is the difference in the high jump by the two different techniques,

b)It will be a two-sided test, as we don't have any particular direction to test.

c)

Vs.,

d)we can use any randomization method, for example, the lottery method, we can draw the required sample from the pot of all the observations written on cards.

e)Since population sd is unknown we will use t-test and the test statistic is given by,

t= = = 1.899

df=n-1=34

p-value=0.067

Since, p-value>0.05, we fail to Reject Ho.

There is insufficient evidence to support the alternative.

CI= = 2.6

=2.62.738

=(-0.138,5.338)