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# hw07_solution - 19.31 Let population 1 be the amount of...

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19.31 Let population 1 be the amount of housework (in hour) wives from two-career families perform weekly last year . Let population 2 be the amount of housework (in hour) wives from two-career 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 p-value < 0.01 (the value of alpha is given) , we reject the null hypothesis. Since p-value = 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 p-value < 0.01 . Since p-value = 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 PG-13. 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 p-value < 0.05, we reject the null hypothesis. Since p-value = 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 PG-13. 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 p-value < 0.05. Since p-value = 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 chi-squared distribution to approximate H distribution.
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