Question

A weight loss program wants to advertise as to the average weight loss after being on their plan for two weeks. A random sample of eleven males was taken. Their weight at the start of the program is recorded, and their weight after two weeks is also noted.

Participant	1	2	3	4	5	6	7	8	9	10	11
Initial Weight	180	210	195	178	200	167	225	242	188	205	192
Post Weight	171	203	197	172	192	162	213	228	188	194	187

(a) Find the paired t interval and check assumptions

(b) Bootstrap the differences

(c) Use walsh averages on the differences.

(d) Which approach is best here and why? Use SAS to help if needed.

Answer 1

a) From the given data,

Initial	Post	Difference
180	171	9
210	203	7
195	197	-2
178	172	6
200	192	8
167	162	5
225	213	12
242	228	14
188	188	0
205	194	11
192	187	5

Descriptive Sstatistics: Difference Total Variable Count Mean StDev Variance Difference 116.82 4.83 23.36

The 95% confidence difference between population means dta,t-4F-6.82 ± 2.228*4.831 /1: (3.5754, 10.0646)

b) By using Boot strap method, the 95% confidece interval is (4, 9455)

StatKey Confidence Interval for a Mean, Median, Std. Dev. Custom Dataset▼ Show Data Table Edit Data Upload File | Change Column(s) Generate 1 Sample Generate 10 SamplesGenerate 100 Samples Generate 1000 SamplesReset Plot Bootstrap Dotplot of Mean Original Sample n= 11, mean= 6.818 median= 7, stdev = 4.834 samples 10000 mean 6.825 std error-1.388 O Left Tail·Two-Tail O Right Tail 15 250 10 200 10 6.818 150 Bootstrap Sample Show Data Table 0.025 0.950 0.025 n= 11, mean= 10.364 median- II, stdev3.957 15 10 100 50 10 6.825 10.364 4.000 9.455

c) Walsches Average difference

Descriptive Statistics: Initial, Post Total Variable Count Mean StDev Variance Initial Post 11 198.36 21.66 469.05 11 191.55 19.15 366.67

e$+21.662 +19.1528.9115 The 95% confidence interval of the difference of two population means s (h-%) ±fo02xl+a2-2-1+4-2-6 -+-= (19836-191.55) ± 2.086 *28.91 1 5 1-+-= (-11.36388 ,25.00024) X1-A2 2 12

4) Best method is paired t test