A simple random sample of students is selected and the stude

A simple random sample of students is selected, and the students are asked how much time they spent preparing for a test. The times (in hours) are as follows: 1.3 7.2 4.2 12.5 6.6 2.5 5.5 Based on these results, a confidence interval for the population mean is found to be µ= 5.7 ± 4.4. Find the degree of confidence.

Solution

Margin of Error = t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
Mean(x)=5.6857
Standard deviation( sd )=3.6785
Sample Size(n)=7
Margin of Error = t a/2 * 3.6785/ Sqrt ( 7)
4.4 = t a/2 * (1.39)
t a/2 = 4.4 / 1.4 = 3.143

From the t-table with 6 degrees of freedom, the two-tailed value that corresponds to 3.143 is .02
Therefore, the level of confidence is 98%