## Related questions with answers

The following data represent the running times of ﬁlms produced by two motion-picture companies:

$\begin{matrix} \text{Company} & \text{Time (minutes) }\\ \text{1} & \text{102} & \text{86} & \text{98} & \text{109} & \text{92}\\ \text{2} & \text{81} & \text{165} & \text{97} & \text{134} & \text{92} & \text{87} & \text{114}\\ \end{matrix}$

Test the hypothesis that the average running time of ﬁlms produced by company 2 exceeds the average running time of ﬁlms produced by company 1 by 10 minutes against the one-sided alternative that the difference is less than 10 minutes. Use a 0.1 level of signiﬁcance and assume the distributions of times to be approximately normal with unequal variances.

Solution

Verified$\bullet$ Let $\overline{x}_{1}$ denotes sample average run time of films produced by company 1.

$\bullet$ Let $\mu_{1}$ denotes true average run time of films produced by company 1.

$\bullet$ Let $n_{1}$ denote the sample size for films produced by company 1.

$\bullet$ Let $s_{1}^2$ denotes sample variance of running time of films produced by company 1.

$\bullet$ Let $\overline{x}_{2}$ denotes sample average run time of films produced by company 2.

$\bullet$ Let $\mu_{2}$ denotes true average run time of films produced by company 2.

$\bullet$ Let $n_{2}$ denote the sample size for films produced by company 2.

$\bullet$ Let $s_{2}^2$ denotes the sample variance of running time of films produced by company 2.

$\star$ We need to determine whether the average running time of films produced by company 2 exceeds the average running time of films produced by company 1 by 10 minutes.

$\star$ We have:

$n_{1}=5$,

$n_{2}=7$.

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