In: Statistics and Probability
Dependent Sample T-Test
Researchers were interested in studying whether seniors who participated in Silver Sneakers had a significant weight loss over a 10 week period. Given the above information, answer the questions below (assume a level of significance of .05).
Paired Samples Statistics |
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Mean |
N |
Std. Deviation |
Std. Error Mean |
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Pair 1 |
preweight Weight before the diet (kg) |
72.53 |
78 |
8.723 |
.988 |
weight10weeks Weight after 10 weeks on the diet |
68.681 |
78 |
8.9245 |
1.0105 |
Beginning Weight in kg |
Weight after 10 weeks in kg |
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Sample Size |
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Sample Mean |
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Sample Standard Deviation |
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Estimated Standard Error |
Using the information below, answer the following questions:
Paired Samples Test |
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Paired Differences |
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Mean |
Std. Deviation |
Std. Error Mean |
95% Confidence Interval of the Difference |
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Lower |
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Pair 1 |
Weight before the diet (kg) - Weight after 10 weeks on the diet |
3.8449 |
2.5515 |
.2889 |
3.2696 |
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Paired Samples Test |
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Paired Differences |
t |
df |
Sig. (2-tailed) |
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95% Confidence Interval of the Difference |
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Upper |
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Pair 1 |
Weight before the diet (kg) - weight10weeks Weight after 10 weeks on the diet |
4.4201 |
13.309 |
77 |
.000 |
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Ho : µd= 0
Ha : µd > 0
................
Level of Significance , α =
0.05 claim:µd=0
sample size , n = 78
mean of sample 1, x̅1= 72.530
mean of sample 2, x̅2= 68.681
mean of difference , D̅ =
3.849
......................
std dev of difference , Sd =
2.5515
std error , SE = Sd / √n = 2.5515
/ √ 78 = 0.2889
......................
t-statistic = (D̅ - µd)/SE = (
3.849 - 0 ) /
0.2889 = 13.323
.......................
Degree of freedom, DF= n - 1 =
77
...................
p-value = 0.0000 [excel
function: =t.dist.rt(t-stat,df) ]
.......................
decision: p-value <α , Reject null hypothesis
conclusion: there is sufficient evidence to say that seniors who
participated in Silver Sneakers had a significant weight loss over
a 10 week period
please revert for doubt