00:01
For this exercise, we are told that the mean number of texts sent and received every day for 18 to 24 year olds is 128.
00:12
And we want to test whether the mean for 25 to 34 year olds differs from the mean for 18 to 24 year olds.
00:21
So let's first establish some hypotheses.
00:26
The null hypothesis is that there is no difference.
00:29
That is that the mean, this is the mean for 25 to 34 year olds, is equal to 128.
00:38
So it's the same as that for 18 to 24 year olds.
00:43
And the alternative hypothesis would be that it differs or that it is not equal to 128.
00:52
And so to test these claims or test these hypotheses, we have a sample of 25 to 34 year olds, which yielded a sample mean number of texts sent and received per day of 118 .9.
01:17
And we are asked to assume a population standard deviation of 33 .17 texts.
01:30
So based on this we are asked to compute a p value.
01:33
The first step is to generate a test statistic.
01:39
And since we are actually given the population standard deviation, our test statistic is therefore based on the standard normal distribution, and it's given as the sample mean minus the null hypothesized mean, divided by the population standard deviation over the square root of the sample size.
02:22
And this comes out to approximately 1 .50.
02:28
Now before calculating the p -value, i'll just note that we, in the question it's stated to test this at a significance level of 0 .05.
02:41
So now to calculate the p value, this is a two -tailed test, and we can tell that by looking at the alternative hypothesis.
02:53
It's a not -equals -to hypothesis, so that indicates a two -tailed test.
02:58
And for a two -tailed test, the p -value is the probability of having gotten a test statistic, at least as extreme as the one that we got, in either the positive or negative directions.
03:10
So this is equal to the probability of z being less than or equal to minus, 1 .5 plus the probability of z being greater than or equal to plus 1 .5.
03:32
And due to the symmetry of the standard normal distribution with it being centered on 0, this is equal to 2 times the probability that z is less than or equal to minus 1 .5...