 Hi, this is Dr. Dunn. I have a problem out of Chapter 7, Section 2, about a population mean. We need to do a test of a claim that a scientist has. And if we read this, it says the scientist estimates the mean nitrogen dioxide level in the city is greater than 33 parts per billion. Key phrase greater than that tells us that this claim must be the alternative because greater than is not a form of equality and the null always has to be a form of equality. We took a random sample of 31 days and we've got the results over here of the mean nitrogen dioxide level we measured. We are told to assume the population standard deviation is 7, given an alpha of 0.11, can you support the scientist's claim, his estimate? First thing we always have to do is to set up the two hypothesis. As I said, the alternative includes a greater than, 33 is the estimate of the population mean, so that is our alternative and it is the claim. And we've got four choices there. These two don't have greater than. Our null has to be the complement of the greater than and that is the less than or equal. So these other ones are wrong. This one is wrong because they said that the null is the claim. So be here is correct. We need to find the critical value from that. We get the rejection region and the standardized test statistic. And then of course we make our decision and a conclusion. So we're going to use the little rectangle up here and we're going to click it and open up this data in StatCrunch. We have the data in StatCrunch in the column labeled VAR1. As we do most often we're going to start with stat and this time it's a Z stat. We have one sample, but this time instead of summary we have the data. So we click on with data. We start out here and I'm going to drag this up a little bit there. We have to select the column. Something a lot of students miss when they use wrong data is they forget to put in the population standard deviation, which we were told was 7. We don't have to worry about grouping. We want to perform hypothesis test. The assumed mean was 33. Our alternative contains the greater than symbol and really we can ignore the rest. We're just going to click on compute and we get our results here. We get our Z standardized test statistic of minus 3.9. We've got a p-value of 1 which tells us this is not anywhere near close to being significant. So right away we know that we would fail to reject the null hypothesis. But let's get the rejection region. So I'm going to go back up to stat, calculators, normal, open up our normal curve here, standard normal curve. We need to enter our alpha. Since this is a right tail test, all of alpha goes into that size. So it's 0.11. We need to select the math operator to point to the right. So there's our rejection region, this red area and it's anything greater than 1.23 if we round that. And as I said, our Z value was minus 3.9 way over here. That's why we're saying this scientist claim is not supported. Hope this helps.