Question

A meteorologist kept track of the number of days it snowed in January. The results were as follows: 4 5 12 9 10 6 5 8 15 9 Find the 95% confidence interval for the mean number of days it snowed? Round the answer to the nearest whole number.

Answer 1

Formula for Confidence Interval for Population mean when population Standard deviation is not known

Given,

x : number of days snowed in January

n : Sample size : 10

	x	(x-)	(x-)2
	4	-4.3	18.49
	5	-3.3	10.89
	12	3.7	13.69
	9	0.7	0.49
	10	1.7	2.89
	6	-2.3	5.29
	5	-3.3	10.89
	8	-0.3	0.09
	15	6.7	44.89
	9	0.7	0.49
Total	83		108.1
Sample mean: = 83/10=	8.3

Sample Mean :	8.3
Sample Standard Deviation : s	3.4657
Sample Size : n	10
Degrees of freedom : n-1	9
Confidence Level :	95
= (100-95)/100	0.05
/2	0.025
	2.2622

95% confidence interval for the mean number of days it snowed

95% confidence interval for the mean number of days it snowed = (5.8207,10.7793)

95% confidence interval for the mean number of days it snowed = (6,11)