1. Parkruns are free 5km timed runs usually run on weekends in different cities, towns and...

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1. Parkruns are free 5km timed runs usually run on weekends indifferent cities, towns and suburbs around the world. It issuspected that they are competitive and hence faster than 5kmfamily fun runs which require payment for registration. Parkrunfinishers do not get medals whereas all family fun run finishersget medals. The summary statistics below are from two randomsamples of 10 park runners and 10 5km family fun runners inBellville. The races were run on the same route and on 2 separatedays but with identical weather conditions. The summary statisticsare for the recorded finishing times (in minutes) of the runners.park runners family fun runners Sample Mean: 20.58 25.67 Samplestandard deviation : 3.5 5.7 (a) Is there evidence that the meanfinishing time differs between the park runners and family funrunners? Perform an appropriate statistical test. (b) Construct a95% confidence interval for the difference between the populationmeans of the two groups. Compare your results to your conclusionsin (a). (c) What assumption(s) are necessary for performing thehypothesis tests and constructing the confidence interval above?Hint: Use a 5% significance level for the F-test but report ap-value for the t-test

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PART A HYPOTHESIS TEST given that meanx2058 standard deviation sd135 numbern110 ymean2567 standard deviation sd2 57 numbern210 null ho u1 u2 alternate mean finishing time differs between the park runners and family fun runners h1 u1 u2 level of significance 005 from standard normal table two tailed t 2 2262 since our test is twotailed reject ho if to 2262 or if to 2262 we use test statistic t xysqrtsd12n1sd22n2 to 20582567sqrt122510324910 to 24064 to 24064 See Answer

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