19.31
Let population 1 be the amount of housework (in hour) wives from twocareer families
perform weekly last year
.
Let population 2 be the amount of housework (in hour) wives from twocareer families
perform weekly this year
.
Since the data is interval and both sample sizes are larger than 30, we can use the t test
to compare the locations of two dependent populations.
Let
μ
1
be the mean of population and
μ
2
be the mean of population. Let
μ
D
equal
μ
1
–
μ
2.
H
0
:
μ
D
= 0
H
1
:
μ
D
> 0
If pvalue <
0.01 (the value of alpha is given)
, we reject the null hypothesis.
Since pvalue = 0.0000
<
0.01
, we reject
the null hypothesis. Thus we can conclude with
90% confidence that there is enough evidence to infer women are doing less house work
now than last year.

If we try to solve the problem by nonparametric method, we use the Wilcoxon Signed
Rank Sum Test. Assume that the two populations have identical spreads and shapes.
H
0
: The two population locations are the same
H
1
: The location of population 1 is to the right of the location of population 2
Since both sample sizes are larger than 30, we can use the normal distribution to
approximate T distribution.
We reject the null hypothesis if the pvalue <
0.01
.
Since pvalue = 0.0000
<
0.01
, we reject
the null hypothesis…(similar to above
conclusion)
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19.39
Let population 1 be the number of rentals for movies that are rated PG13.
Let population 2 be the number of rentals for movies that are rated R.
Since the data is interval and both sample sizes are larger than 30, we can use the t test
to compare the locations of these two dependent populations.
Let
μ
1
be the mean of population and
μ
2
be the mean of population. Let
μ
D
equal
μ
1
–
μ
2.
H
0
:
μ
D
= 0
H
1
:
μ
D
> 0
If pvalue < 0.05, we reject the null hypothesis.
Since pvalue = 0.0000
< 0.05, we reject
the null hypothesis. Thus we can conclude with
95% confidence that there is enough evidence to infer the average rental of movies that
are rated R is higher than that of movies that are rated PG13. By adding sexually
explicit scenes may increase the movie’s appeal and profitability.

If we try to solve the problem by nonparametric method, we use the Wilcoxon Signed
Rank Sum Test. Assume that the two populations have identical spreads and shapes.
H
0
: The two population locations are the same
H
1
: The location of population 1 is to the left of the location of population 2
Both sample sizes are larger than 30, so we can use the normal distribution to
approximate T distribution.
We reject the null hypothesis if the pvalue < 0.05.
Since pvalue = 0.0000
< 0.05, we reject
the null hypothesis…. (similar to above
conclusion)
19.45
H
0
: the locations of the 4 populations are the same
H
1
: At least two population locations differ
Assume that the four populations have identical spreads and shapes. As sample sizes
are all larger than 5, we can use chisquared distribution to approximate H distribution.
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 Fall '11
 游啟璋
 Normal Distribution, Null hypothesis

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