00:01
So question a, we want to know what is the unknown parameter that we're testing? and it is a p value, and that is the proportion of homeowners in, proportion of homeowners in new homes, new homes in richland, washington with heat pumps.
00:30
And part b asks for you to state the null and alternative hypothesis.
00:42
So we're going to assume that the building states that the proportion is equal to 0 .7, and alternately it says, do we have it that is less than that? so the proportion is less than 70%.
00:56
Part c says to check the conditions.
01:00
Well, we should have a simple random sample, and we have the number of successes and the number of failures should be at least 10.
01:13
And we have, we would have that, we have that p hat being 32 out of 58.
01:21
And so that is sufficiently large, and we're not having more than 5 % of the entire population of the number of cities.
01:30
So we should be approximately normal distribution.
01:34
So now part d, we want to list what the test statistic is, and why don't we change color here.
01:41
So that z value, if i can get that to change, will be that 32 out of 58 minus the 0 .7 divided by the square root of 0 .7 times its complement over the sample size.
01:56
And let me quick enter that in for you, and i'm actually going to put this into my calculator as a one proportion z test...