Question

(10 marks) For a study of balance in elderly people, a researcher randomly selected 20 consenting individuals over the age of 70 from a local community centre. Each participant stood on a “force platform”. They were instructed to press a hand-held button as quickly as possible in response to hearing a randomly timed buzzer. The subsequent forward-backward sway of the individuals was measured (in mm). The researcher would like to know whether elderly people sway more than 18 mm (the typical distance observed on younger people), on average. In her sample, the average sway was 20.4 mm. For the purposes of this question, you may assume that sway measurements are normally distributed with a standard deviation of 4 mm.

a. (2 marks) What are the null and alternative hypotheses?

b. (1 mark) What is the value of the test statistic?

c. (1 mark) What is the p-value?

d. (2 marks) Provide an interpretation of your p-value in c).

e. (2 marks) Using a significance level of ?? = 0.05, state your conclusions in the language of the problem.

f. (2 marks) Name the key unstated assumption required for the validity of your hypothesis test and explain why it is reasonable in this context.

Answer 1

Solu tion Given (a) Necs tstates the null and altemative hyfathesis Nu yfathesis Ho: A<18 Atemative hyfathesig H,: H >8 |b) Noa t° find the Value of the test- statistic X-H Test- statistig 20-4 0.8944 2.68 Theoefie the Value of the test -statistic, 2.68 9 Noo tfind te P-value tteae usin the Values of test- statistic ter& (o-es) then Ge get the P-alue Sigwifiance amd (89 f-Vahue (-: nateiled) d.003

mae fobability of Jeting the test- statistic the extneme of e2ual me was Smm aveaage ay Value obseoved auming that ) Deasion P-Value (o.00 37) lo-05 Since the f-Value is les then the Sigwificaace levek thenefte Cse njedt the l hyfathesi3(Ho) Condusion We have Sufficient ithe fav of the daim eviden ce tha t ldey feole aay mle than 18 mm
Note:As per HomeworkLib rules 5 bits enough.Due to little confussion about f bit so i couldn't solved.If you want to answer for f bit please post it separately.

Thank you.