a. Many travellers arrange their travel plans over the internet. A recent survey of 1000 randomly selected respondents reported that 55% purchased plane tickets over the internet.
i. Find the 99% confidence interval estimate of the population proportion of travellers who purchase plane tickets over the internet.
ii.Use the appropriate Excel workbook from Estimators.xls to construct the same interval as was required in part (i). Include the resulting Excel output. Highlight the upper and lower limits of the confidence interval in this output.
b. A company wants to determine the sample size required to estimate a company’s average ordering lead time to within 1 day with 95% confidence. If the standard deviation of ordering lead times is known to be 7 days, determine the required sample size.
In tennis, the Review system is used to determine whether a tennis ball is out of bounds or not and can be used to overturn or confirm calls by the umpire. In one of the first uses of the system at a particular major tournament, players made 741 challenges and 274 of these were successful in overturning the umpire’s call.
i. Using a 1% significance level test the claim that the proportion of successful challenges is greater than one in three.State clearly the null and alternative hypotheses, the test statistic, test result, decision rule and conclusion in terms of the original problem.
ii. What condition/s must be met to justify using the standard normal distribution for this hypothesis test?
iii Use the appropriate Excel macro in Test Statistics.xls to again perform the hypothesis test in part (i). Present the output generated by Excel as your answer here
iv Explain how this output verifies your conclusion in part (i) by reference to the p value of the test.
A simple random sample of the birth weights of 80 piglets in a regional piggery gave a mean weight of 3265 gm with a standard deviation of 451 gm.
i. Construct a 95% confidence interval estimate of the population birth weight of piglets born at this piggery
ii. Use the appropriate Excel work book from Estimators.xls to construct the same interval as was required in part (i). Include the resulting Excel output. Highlight the upper and lower limits of the confidence interval in this output.
