00:01
Okay, so we're looking to investigate whether or not the mean of the age at which american men get married has increased or not since a survey that was done in the past.
00:09
A recent survey has been done in which the mean was 24 .2, bigger than the older mean at 23 .3 and the standard deviation was 5 .3.
00:18
And this was a sample of 40 people.
00:22
So part a wants us to construct the alternative hypotheses.
00:26
So if i call the new mean, the current mean, age of men getting married.
00:31
Married, mu -tilda, then the null hypothesis is that this is the same as the old mean new.
00:40
The alternative hypothesis is that it's greater than the old mean.
00:45
Part b asked us to state our assumptions that we're using, so we're using the central limit theorem because our sample size is greater and equal to 40, so we can assume some normal distribution.
00:57
Part c then asks us to calculate the test statistic and p -value.
01:01
Now the test statistic is going to be given by the sample mean minus the population mean divided by the sample standard deviation over the square root of the sample size.
01:15
And if you plug that in, you can find z is 1 .07.
01:23
So that means that in the scheme of the normal distribution of sample means, this sample mean, this x bar 24 .2 lies here.
01:38
And the p value for z equals 1 .07, you can check is 0 .857 to four decimal places.
01:48
And so what that means is that x bar equals 24 .2 lies here.
01:55
And means less than that are 85 .77, happened 85 .77 % of the time.
02:14
Part d asks us to compare the p value to the significance level...