The average credit card debt for a recent year was $9205. Five years earlier the average credit card debt was $6618. Assume sample sizes of 35 were used and the standard deviations of both samples were $1928. Is there enough evidence to believe that the average credit card debt has increased? Use alpha = 0.05 give a possible reason as why or why not the debut was increased.

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Asked Nov 25, 2019
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The average credit card debt for a recent year was $9205. Five years earlier the average credit card debt was $6618. Assume sample sizes of 35 were used and the standard deviations of both samples were $1928. Is there enough evidence to believe that the average credit card debt has increased? Use alpha = 0.05 give a possible reason as why or why not the debut was increased. 

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Expert Answer

Step 1

Given data

Recent year
5 years later
Sample
Sample standard deviation
Sample size
9205
6618
mean
1928
1928
35
35
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Recent year 5 years later Sample Sample standard deviation Sample size 9205 6618 mean 1928 1928 35 35

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Step 2

Formulation of Hypothesis

Null Hypothesis:- There is no difference in the average credit card debt

i.e. H0: µ1= µ2

Alternative Hypothesis: - average credit ...

Ху — X1
9205 6618
t =
= 5.613
19282
19282
35
35
Пу
п2
d.o.f 35+35-2 68
Calculating the p-value
p-value 0 (From Excel-T.DIST.RT (5.613,68))
p-value 0.05
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Ху — X1 9205 6618 t = = 5.613 19282 19282 35 35 Пу п2 d.o.f 35+35-2 68 Calculating the p-value p-value 0 (From Excel-T.DIST.RT (5.613,68)) p-value 0.05

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Hypothesis Testing

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