00:01
Hello student, in the given question, the given values are the null hypothesis is mu equals to 90 versus the alternative hypothesis is mu is not equal to 90.
00:18
Means this is two -tailed test.
00:20
N equals to 16, x bar is equals to 86 .3, sigma is equals to 6 .1 and alpha value is equals to 0 .05.
00:33
We have to assume that the population is normally distributed and we have to find first the critical value, second the test statistic, third the p -value and fourth conclusion.
01:09
So here we use test statistic.
01:17
First we have to find the test statistic.
01:18
From test statistic we have to calculate the critical value and p -value.
01:22
So first we find out the test statistic.
01:25
So here we use t -test for two samples.
01:34
So t equals to x bar minus mu upon sigma upon under root of n.
01:42
Sorry, t -test for one sample.
01:44
Here we use t -test for one sample.
01:50
So substituting values in this formula, x bar is 86 .3 minus 90 divided by 6 .1 upon under root of 16.
02:04
So t equals to minus 2 .62.
02:06
Then critical value is critical value of p for the two -tailed test at 5 % level of significance with 15 degrees of freedom using t -distribution table...