Question 4. 17 marks] IChapter 6 A statistics student was interested in investig

Question

Question 4. 17 marks] IChapter 6 A statistics student was interested in investigating how long it takes to get a pizza delivered from the local pizzeria. Over a few weeks, a random sample of 10 delivery times (in minutes) was recorded. The data are displayed below: 28.4, 27.2, 19.6, 32.9, 16.3, 29.7, 18.5, 27.4, 19.8, 23.8 Summary Statistics: Calculate and interpret a 95% confidence interval for the mean delivery time. 24.36 minutes. And s 5.56 (a) 6 Marks Note: You must clearly show that you have followed the "step-by-step guide to producing a confidence interval by hand given in the Lecture Workbook, Chapter 6. Use the -procedures tool to find values for i-multipliers and standard errors. A friend of the statistics student pointed out to them that their confidence interval must be wrong as ..more than half the values used to calculate t were not in the 95% interval, so how can they have 95% confidence in the interval?" Explain what was wrong with this thinking (b) I Mark]

Explanation / Answer

A)

Standard error of the mean = SEM = S/N = 1.758

t(, N-1) = 2.262

Confidence interval = m +/- (t(, N-1)*SEM)

Mean = 24.36

Lower bound: 20.38

Upper bound: 28.34

b)in confidence interval statistic vary between lower and uppeupper bound not half values

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