00:01
So our question says that the water underground reported that the mean water of summer rainfall for the north and us is at least 11 .52 inches.
00:09
Ten cities in the northern east are randomly selected and the mean rainfall amount is calculated to be 7 .4 inches with a standard division of 1 .3 inches.
00:18
At 5 % level of significance, can it be concluded that the mean rainfall was reported was below average, we should also perform this test at 1 % level of significance and make our conclusion.
00:29
So our population mean is 11 .52.
00:33
The sample size is 10.
00:35
The sample mean is 7 .42 and the sample standard deviation is 1 .3.
00:40
So the first step is to state our null and alternative hypothesis.
00:45
So we have that h0 is that m is equals to 11 .52 and the alternative is based on the fact that m is lesser than 11 .52.
00:55
So before we move on, we need to set our decision rule which is important to help us to whether we are going to accept or rejects the null hypothesis and i'll be using the p -value method to make my decision and it states that if our p -value is greater than alpha we are going to accept the null hypothesis and if our p -value is lesser than alpha we are going to reject the null hypothesis so before we can be able to get our pay value we need our test statistics now our test statistics is going to be a t -t test and this is because number one the sample size which is then is actually lesser than 30 and number two we don't know the value of the population standard deviation hence you'll be making use of this a value of the sample standard deviation and which is 1 .3 so this is our test statistic is given to us as t is equals to xbara minus md divided by s divided by the square root of n so it's time to substitute our parameters so we have 7 .2 minus our population means 11 .52 divided by our sample star division is equal to 1 .3 divided by the square root of 10 so our t is equal to 7 .42 minus 11 .52 and that gives us a minus 4 .1 divided by so 1 .3 divided by the square root of 10 that gives us 0 .411 .0 9 so when we do the math here we have minus 1 .1 by 0 .411 .09 and we have our answer to be minus 9 .9733.
02:45
So this is the value of our test statistics.
02:48
So the next step is for us to get the pay value and to get the pay value, i'll be making use of a calculator to get the pay value of those test statistics...