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Given the following data for utilisation and time spent in system for the Able-Baker carhop problem. Calculate the overall point estimators, standard error and 95% confidence interval for the same.

Given t$_{0.025,3}$=3.18

Run r 1 2 3 4
Able's Utilization $\rho _r$ 0.808 0.875 0.708 0.842
Average system time w$_r$ (mins) 3.74 4.53 3.84 3.98
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Part - I

Given that the four estimates, $\overline{\rho_r}$ of Able's utilization

  1. Compute overall point estimate

    $\begin{aligned} \hat{\rho_r} &= \frac{1}{R} \sum_{r=1}^R \space \hat{P_r} \\ &= \frac{1}{4} (0.808 + 0.875 + 0.708 + 0.842) \\ &= 0.808 \end{aligned}$

  2. Compute the estimate of variable of $\hat{\rho}$

    $\begin{aligned} \hat{\sigma}^2 (\hat{\rho}) &= \frac{1}{(R-1)} \sum^R_{R_{r-1}} …

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