00:01
A simple random sample of 49 adults is obtained from a normally distributed population and each person's red cell count has a sample mean of 5 .31 and a sample standard deviation of 0 .54.
00:14
Use a significance level of 0 .01 to test the claim that the sample is from a population with a mean less than 5 point.
00:22
I'm going to assume that means yeah less than 5 .4 so our null hypothesis is going to be that the mu is equal to 5 .4 and our alternative is that the mean is our mu is less than 5 .4.
00:36
So our test statistic is going to be a t -test statistic and we'll take 5 .31 minus 5 .4 we'll divide that by our standard deviation over the square root of our sample size.
00:54
So our test statistic is negative 1 .17.
00:59
I hope they want it to three decimal so negative 1 .167 is what we'll use.
01:07
And what is the conclusion to the claim? well i'm going to go ahead and use a p -value approach so my p -value is 0 .1246 and that is larger than my significance level and if the claim is that we are less than 5 .4 then we're going to say do not reject the null hypothesis.
01:32
There is insufficient evidence to support the claim.
01:46
And then for problem number two so that was problem number one.
01:51
Problem number two the ages of actresses when they won an acting award is summarized by the statistics given.
02:00
We're going to use a significance level of 0 .01 to test the claim that the mean age of the actress when they win an award is 32 years.
02:13
So in this case it's a little bit tough to see because there's a strange doubling of values.
02:26
So i think this is supposed to be n equals 80, x bar equals 35 .1, standard deviation is 11 .3 and the significance level is 0 .01.
02:39
Our null hypothesis would be that mu is equal to 32 and our alternative is that mu is different from 32.
02:49
So in this case our null hypothesis is our claim.
02:54
Our test statistic is going to be 35 .1 minus 32 over the quantity of 11 .3 divided by the square root of 80.
03:02
Now it's possible that that sample size is supposed to be 81 because it says 80 81...