00:01
In this question, the random samples from a normal distribution is given.
00:05
We have to find the 95 % confidence interval for the population mean mu.
00:11
So the samples are 3 .357 .99.
00:22
So to find the confidence interval, first we need to find x bar, that is 3 plus 3 plus 5 5 plus 7 plus 9 plus 9 divided by 6 that is 36 divided by 6 6 so the x bar is sample mean is 6 so we have to find standard deviation of the sample using the equation summation x i minus x bar the hall square divided by n minus 1 so this is equal to 2 .7 5, 7.
01:02
So we got the sample standard deviation also.
01:08
Here we know that the population standard deviation sigma is unknown.
01:13
So we have to use the t distribution.
01:18
So the 95 percentage confidence level is equal to 0 .95.
01:27
So alpha is 1 minus 0 .95 which is equal to 0 .05.
01:34
So we have to find corresponding t alpha by 2.
01:38
We'll get this using the excel equation.
01:41
Now we can see that for alpha equal to 0 .05 the corresponding critical value is 2 .575 that is approximately 2 .571.
01:56
So we got the critical value.
01:58
Next we can find the confidence interval...