Question

Write a confidence interval problem using one of the options below.

Think about a population mean that you may be interested in and propose a confidence interval problem for this parameter. Your data values should be approximately normal.

30 random households were given a survey and asked how many times a month each household went grocery shopping (confidence interval for the population mean is 95%). The following answers were given:

1 Time- 1

2 Times- 3

3 Times- 3

4 Times- 19

5 Times- 3

6 Times- 1

Answer 1

The sample mean and sample standard deviation here are computed as:

X	N	X*N	(X- MEAN(X))^2	N*(X-MEAN(X))^2
1	1	1	7.65	7.65
2	3	6	3.12	9.36
3	3	9	0.588	1.76
4	19	76	0.0544	1.03
5	3	15	1.52	4.56
6	1	6	4.99	4.99
		113		29.4

For n-1 = 29 degrees of freedom, we get from the t distribution tables that:

P( -2.045 < t₂₉ < 2.045 ) = 0.95

Therefore the confidence interval here is computed as:

(3.3908, 4.1426)

This is the required 95% confidence interval for the population mean.