Download Inferences based on two samples

Inferences based on two samples
A new weight-reducing technique, consisting of a liquid protein diet, is currently
undergoing tests by the Food and Drug Administration (FDA) before its introduction into
the market. A typical test performed by the FDA is the following: The weights of a
random sample of five people are recorded before they are introduced to the liquid
protein diet. The five individuals are then instructed to follow the liquid protein diet for 3
weeks. At the end of this period, their weights (in pounds) are again recorded. The results
are listed in the table.
Person Weight before diet Weight after diet
1 150
143
2 195
190
3 188
185
4 204
200
5 197
191
a. Find Xd (the sample mean of the differences)
Column1
Mean
Standard Error
Median
Mode
Standard
Deviation
Sample
Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
-5
0.707107
-5
#N/A
1.581139
2.5
-1.2
0
4
-7
-3
-25
5
Use Excel, we get the above table, we know that the sample mean of the differences is
Xd=-5.
b. Find Sd
(the sample standard deviation of the differences)
Use Excel, we get the above table in part a) , we know that the sample standard deviation
of the differences is Sd=1.581139
c. Test to determine if the diet is effective at reducing weight. Use alpha= .10.
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean
Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Variable
1
186.8
455.7
5
0.998443
Variable
2
181.8
499.7
5
0
4
7.071068
0.001055
2.131847
0.002111
2.776445
Use Excel, we get the above table. From the table, we know that the pvalue=0.001055<0.10, so we should reject the null hypothesis. We conclude that the diet
is effective at reducing weight.