Question

1.Menstrual cycle length. Menstrual cycle lengths (days) in an SRS of nine women are as follows: {31, 28, 26, 24, 29, 33, 25, 26, 28}. Use this data to test whether mean menstrual cycle length differs significantly from a lunar month using a one sample t-test. (A lunar month is 29.5 days.) Assume that population values vary according to a Normal distribution. Use a two-sided alternative. Show all hypothesis-testing steps.

Answer 1

olution:

x	x2
31	961
28	784
26	676
24	576
29	841
33	1089
25	625
26	676
28	784
∑x=250	∑x2=7012

Mean ˉx=∑xn

=31+28+26+24+29+33+25+26+28/9

=250/9

=27.7778


Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√7012-(250)29/8

=√7012-6944.4444/8

=√67.5556/8

=√8.4444

=2.9059

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 29.5

Ha :     29.5

Test statistic = t

= ( - ) / S / n

= (27.78 -29.5) / 2.90 / 9

= -1.779

Test statistic = t = -1.779  

P-value =0.1131