A new? weight-loss program claims that participants will lose an average of more
ID: 3368735 • Letter: A
Question
A new? weight-loss program claims that participants will lose an average of more than 10 pounds after completing it. The accompanying data table shows the weights of eight individuals before and after the program. Complete parts? (a) through? (e) below.
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a. Perform a hypothesis test using
alpha?equals=0.050.05
to determine if the average weight loss was more than 10 pounds for participants in the? weight-loss program. Let
mu?d
be the population mean of? matched-pair differences for the weight before the program minus the weight after the program. State the null and alternative hypotheses. Choose the correct answer below.
A.
Upper H 0H0?:
mu Subscript d?dless than or equals?10
Upper H 1H1?:
mu Subscript d?dless than<10
B.
Upper H 0H0?:
mu Subscript d?dequals=10
Upper H 1H1?:
mu Subscript d?dnot equals?10
C.
Upper H 0H0?:
mu Subscript d?dnot equals?10
Upper H 1H1?:
mu Subscript d?dequals=10
D.
Upper H 0H0?:
mu Subscript d?dless than<10
Upper H 1H1?:
mu Subscript d?dgreater than or equals?10
E.
Upper H 0H0?:
mu Subscript d?dless than or equals?10
Upper H 1H1?:
mu Subscript d?dnot equals?10
F.
Upper H 0H0?:
mu Subscript d?dless than or equals?10
Upper H 1H1?:
mu Subscript d?dgreater than>10
Table:
Person
Before
After
1
227
201
2
213
195
3
206
193
4
187
171
5
204
195
6
198
180
7
242
230
8
191
192
Person
Before
After
1
227
201
2
213
195
3
206
193
4
187
171
5
204
195
6
198
180
7
242
230
8
191
192
Explanation / Answer
Hypothesis:
H0 : mud <=10
Ha : mud > 10
Before after dbar
227 201 26
213 195 18
206 193 13
187 171 16
204 195 9
198 180 18
242 230 12
191 192 -1
dbar = ?(before) - ?(after) = 13.875
s(dbar) = 7.8819
SE = s(dbar)/sqrt(n) = 2.7867
Test Statisitcs,
t = dbar/SE
= 13.875/2.7867
= 4.9790
degrees of freedom = n-1 = 7
p value = .0008
Reject the null hypothesis
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