00:01
So, in the given question, we have to construct a 95 % confidence interval for the population mean.
00:07
Now, we have here a sample of size 32, the mean of the sample is 39 .6 and the sample standard deviation is 8 .4.
00:17
So, for a confidence level of 95%, alpha is 1 -0 .95 that is equal to 0 .05, right.
00:26
Now, the critical value here, this corresponds to the value of t alpha by 2 n -1 and this is equal to t 0 .02531 that is 2 .040, right.
00:41
Now, the formula for the confidence interval is sample mean plus minus critical value into standard deviation upon square root of sample size.
00:50
So, this is 39 .6 plus minus 2 .040 into 8 .4 upon square root of 32.
01:00
So, this is equal to 39 .6 plus minus 3 .029 that is equal to 36 .57 and 42 .63, right...