Question

Data for problem:
Column C

210
125
180
225
160
170
190
195
140
160

   Column D

211
121
185
222
157
174
184
194
133
165

You are measuring weight loss using the same set of people at different times C and D. You want to know whether there is any difference in the weight between the start of the diet and the end of the diet. Column C gives the weight at the beginning of diet time. Column D gives the weight for the SAME person at the end of the diet time. Since there is data for the same person at different times, we will test whether µ(C-D) <= 0 or µ(C-D) > 0 (meaning the diet did cause weight loss) since we have correlated data (matched pairs).

1. Make a new series of data samples by letting E = C – D. List your new series of 10 numbers.
2. What is the null hypothesis H₀ ?
3. What is the alternative hypothesis H_a ?
4. What type of tail test are we going to use? (left tail, right tail, two tail)
5. What is the mean xbar of this new sample?
6. What is the standard deviation of the sample s?
7. What is the size of the sample n?
8. How many degrees of freedom does this data set have?
1. What is the t-statistic for this sample?
10. Use the t-distribution calculator to compute a p-value. Show a screen shot of your answer.
11. Based on this value of p and using a 99% confidence level, is there a systematic difference in the weight changes between the start and stop time of the diet? Should we accept or reject the null hypothesis?

Answer 1

C	D	C-D
210	211	-1
125	121	4
180	185	-5
225	222	3
160	157	3
170	174	-4
190	184	6
195	194	1
140	133	7
160	165	-5

b)

c)

d)

this is two-tailed test

e)	mean	0.9
f)	sd	4.45845
g)	n	10
h)	df	9

i)TS = (Xbar)/(Sd/sqrt(n)) = 0.9/(4.45845/sqrt(10))

= 0.63835

j)

p-value = t.dist.2t(0.63835,9)

= 0.5391

k)

since p-value > alpha (0.01)

we fail to reject the null hypothesis

we conclude that there is no significant difference