Question

34. The following data show the number of hours per day 12 STAT 3309 students spent in front of screens watching​television-related content. Use the printout below to answer the following​ question:

HOURS
1.2	Mean	4.666666667
4.8	Standard Error	0.695802712
4.1	Median	4.75
4.7	Mode	​#N/A
7.9	Standard Deviation	2.410331299
7.5	Sample Variance	5.80969697
5.1	Kurtosis	​-1.182783193
2.3	Skewness	0.141232566
5.8	Range	7.1
1.9	Minimum	1.2
2.4	Maximum	8.3
8.3	Sum	56
	Count	12
	Confidence​ Level(95.0%)	1.531451444

What is the​ 95% confidence interval​ (to the nearest​ hundredth) for​ µ?

A.

​(3.30, 6.03)

B.

​(1.20, 8.30)

C.

​(3.97, 5.36)

D.

​(3.14, 6.20)

Answer 1

Solution:

Given :

Sample Mean =

Standard Error = SE = 0.6958027

n = sample size = 12

c = confidence level = 95%

Formula for confidence interval is:

where

We need to find tc value for c = 95% confidence level.

two tail area = 1 - c = 1 - 0.95 = 0.05

df = n - 1 = 12 - 1 = 11

look in t table for df = 11 and two tail area = 0.05 and find corresponding t critical value.

t_c = 2.201

Thus

Thus

Thus the 95% confidence interval for µ is :

Thus correct option is : D. ( 3.14 , 6.20)