Advanced Business Statistics

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Advanced statistics stat201

The operation manager of a company that manufactures shirts wants to determine whether there are differences in the quality of workmanship among three daily shifts. She randomly selects 427 recently made shirts and carefully inspects them. Do these data provide sufficient evidence to infer that there is a relationship between quality and the three shifts? Use 1% significance level. ShiftShirt condition 1...
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1. Tíme spent serving a customer at a cafe is normally distributed, with $\mu=7$ minutes and $\sigma=1.8$ minutes.(a) If you select a random sample of duration serving twenty-five ( 25 ) customers, determine the probability that the sample mean is between 6.8 and 7.2 minutes.(b) If you select a random sample of 144 customers, determine the probability that the sample mean is between 6.8 and 7.2 minutes.(c) Explain the difference in the results of (i) and (ii).
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A factory manager collected a sample of ten (10) packets of 3 -in-1 coffee and the weights (in grams) of each packet are recorded as follow.$\begin{array}{lllll}25 & 23 & 26 & 28 & 24 \\ 21 & 26 & 24 & 25 & 27\end{array}$Calculate(a) the mean weight of a packet of 3 -in-1 coffee.(b) the sample standard deviation of the data collected.(c) find a $90 \%$ confidence interval for the weights of the 3 -in- 1 coffee.

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A service counter manager wishes to ensure that an average of 16 seconds to serve a customer. In order to analyse the efficiency of the service process, he takes a random sample of 56 customers. The mean service time of the sample is 15.8 seconds. Assume that the population standard deviation is 0.8 seconds.(a) State the null and the altemative hypotheses for the test.(b) Use the p-value approach to test the manager's concem at $\alpha=0.05$.(c) Confim your result in (ii)...