Statistical Inference

1) The BelSante Company operates retail pharmacies in 10 Eastern states. Recently, the company’s internal audit department selected a random sample of 300 prescriptions issues through a system. The objective of the sampling was to estimate the average dollar value of all prescription issued by the company. The following data were collected:

x ̅=$14.23

a) Determine the 90% confidence interval estimate for the true average sales value for prescriptions issued by the company. Interpret the interval estimate.
b) One of its retails outlets recently reported that it had monthly revenue of $7,392 from 538 prescriptions. Are such results to be expected? Do you believe that the retail outlet should be audited? Support your answer with calculation and logic.
2) The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she has collected a random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750.
a) Develop the appropriate null and alternative hypotheses.
b) Assuming the standard deviation is known to be $2,500 and the significance level for the test is to be 0.05, what is the t-statistic?
c) What is the conclusion? Is the average starting salary less than $30,000 per year?
3) An Internet business prides itself in its ability to fill customer’s orders in six calendar days or less on average. Periodically, the operations manager selects in a random sample of customer orders and determines the number of days required to fill the orders. Based on the sample information, she decides if the desired standard is not being met. She will assume that the average number of days fill customer orders is six or less and less the data suggest strongly otherwise.
a) Establish the appropriate null and alternative hypotheses.

b) On one occasion where sample of 40 customers were selected, the average number of days was 6.65, with the standard deviation of 1.5 days. Can the operations manager conclude that her Internet business is achieving its goal? Determine your answer using a 90% confidence level.
4) For the United States, the mean monthly Internet bill is $65.72 per household. A sample 50 households in a southern state showed a sample mean of $63.22. Using a standard deviation of $6.72, and a significance level of .05, with a resulting p-value of .005689, are these household significantly smaller than the mean?

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