Question

The data in the table below are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag.

X	Freq.
1	1
2	7
3	18
4	7
5	6

Construct a 95% confidence interval for the true mean number of colors on national flags.

Fill in the blanks on the graph with the areas, the upper and lower limits of the Confidence Interval and the sample mean. (Round your answers to two decimal places.)

	CL =
α 2 =		α 2 =

Answer 1

Need to calculate mean and SD first

	Value, x	Frequency, f	x*f	x-Mean	(x-Mean)^2	(x-Mean)^2*f
	1	1	1	-2.25641	5.0913872	5.091387245
	2	7	14	-1.25641	1.5785667	11.04996713
	3	18	54	-0.25641	0.0657462	1.183431953
	4	7	28	0.74359	0.5529257	3.870479947
	5	6	30	1.74359	3.0401052	18.24063116
Total	15	39	127	-1.28205	10.328731	39.43589744
Mean	127/39 = 3.25641
Variance	39.43589744/38 =1.037787
SD	1.018718

To calculate 95% confidence interval, we need to find tc (Critical t value) as population standard deviation is not given

For 95% CI and dof = n-1 = 39 -1 = 38, tc = 2.024

Confidence Interval is given by

So,

Lower limit = 2.93

Upper Limit = 3.59

Sample Mean = 3.26

Please let me know if you have any doubts. Happy to help. Please thumbs up if you like the solution. Thanks