00:02
In order to conduct a hypothesis test for the population mean, a random sample of 12 observations is drawn from a normally distributed population.
00:11
The resulting sample mean and sample standard deviation are calculated as 16 .6 and 2 .2 respectively.
00:29
Our null hypothesis is that the mu is less than or equal to 14 .9 versus the alternative that the mu is greater than 14 .9.
00:45
Calculate the value of the test statistic.
00:52
So t is equal to 16 .6 minus 14 .9 divided by 2 .2 over the square root of 12.
01:01
And that is 2 .677.
01:09
Find the p -value.
01:13
So the p -value is between 0 .01 and 0 .025.
01:37
At the 5 % significance level, what is the conclusion? so if alpha is 0 .05, we are going to reject the null hypothesis since the p -value is less than the significance level.
02:06
And then interpret the result at 0 .05.
02:11
So we conclude that the population mean is greater than 14 .9.
02:18
Now we have a new hypothesis statement...