Question

A study is run to estimate the average number of toilet paper rolls a typical U.S. household currently have. Say a sample of 10 households is selected last month and they reported the number of toilet paper (in rolls) as follows.

                       75         56        50        94        65       111      97        88            103        98

1. Assume the average amount of toilet paper a household usually have is 55 rolls at national level. Test whether the mean number of toilet paper rolls in this sample is significantly different from the national level? Use alpha level of .05.
2. Based on your results from part (a), without calculating the confidence interval, describe how the confidence interval of the average number of toilet paper at national level.  (Hint: interpret the meaning of confidence interval in relation to a hypothesis test.)

Answer 1

Solution:

x	x2
75	5625
56	3136
50	2500
94	8836
65	4225
111	12321
97	9409
88	7744
103	10609
98	9604
---	---
∑x=837	∑x2=74009

Mean ˉx=∑xn

=75+56+50+94+65+111+97+88+103+98/10

=83710

=83.7

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

=√74009-(837)210/9

=√74009-70056.9/9

=√3952.1/9

=√439.1222

=20.9552

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 55

Ha :     55

Test statistic = t

= ( - ) / s / n

= (83.7-55) / 20.95/ 10

= 4.332

Test statistic = t = 4.332

P-value =0.0019

= 0.05  

P-value <

0.0019 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that