Question 4. [7 marks] [Chapter 6]

A statistics student was interested in investigating the average time it takes to get a pizza delivered

to their house from the local pizzeria. Over a few weeks, a random sample of 10 delivery times

(in minutes) was recorded. The data are displayed below:

17.8, 23.1, 18.7, 24.7, 31.5, 22.3, 17.9, 20.3, 28.4, 27.2

Summary Statistics: x = 23.19 minutes and s = 4.72.

(a)

Calculate and interpret a 95% confidence interval for the mean delivery time. [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 t-procedures

tool to find values for the t-multiplier and standard error.

(b)

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 it were not in the 95% interval, so

how can they have 95% confidence in the interval?" Explain what was wrong with this

thinking.

[1 Mark]

Step-by-Step Guide to Producing a Confidence Interval by Hand

1. State the parameter to be estimated. (Symbol and words)

Is it , p, 1 - 2, or p1 - p2?

2. State the estimate and its value.

3. Write down the formula for a CI, estimate t se(estimate), from the Formula Sheet

4. Use the appropriate standard error. (Will be provided)

5. Use the appropriate t-multiplier. (Will be provided)

6. Calculate the confidence limits. (End points of the confidence interval)

7. Interpret the interval using plain English.

Use the confidence limits to construct an answer to the original question in plain English.