00:01
Hello students, given that x bar is equal to 133, s is given as 28.
00:09
In a part of the question, the sample size is 40.
00:14
Here we want to find 90 % confidence interval.
00:18
At 90 % confidence level, t critical value is, we have alpha is equal to 1 minus 0 .90 which is 0 .10.
00:29
Therefore, alpha by 2 is 0 .05.
00:34
Here the degrees of freedom is n minus 1 which is 40 minus 1 which is equal to 39.
00:42
Therefore, t critical is t alpha by 2 degrees of freedom which is equal to t 0 .0539.
00:52
From the table, the value is 1 .685.
00:57
Therefore, 90 % confidence interval, the formula is given by x bar plus or minus t alpha by 2 into degrees of freedom into s by root n.
01:15
Now, substitute the values into the formula, we will get it as 133 plus or minus 1 .685 into 28 divided by root 40.
01:29
This is equal to 133 plus or minus 7 .4598.
01:38
Therefore, the confidence interval is 125 .54, 140 .46.
01:51
The 90 % confidence interval for the population mean when n equal to 40 is from a lower limit of 125 .54 to an upper limit of 140 .46...