So for this problem we are given the following table from a stack crunch output And we want to use alpha is equal to 0.05 And the claim is the normal range of pulse rates among adults is typically given as 60-100 beats per minute. This results in our standard deviation equals 10 beats per minute. Well, we want to do here is we want to identify the null hypothesis, the alternative hypothesis, the testes cystic, the P value and possible any critical values we can get and then make a conclusion based on the results given for our data. Before I begin, I would like to hope everyone remembers what the definition of alpha is. So awful is the level of significance is also A Type one error which is defined as the probability to reject your no hypothesis given you're no hypothesis is true or having a false positive. Yeah. All right. So we have a alpha level of 0.05. We have a degrees of freedom of 152 recalled. We can find the degrees of three and that is artist and minus one. So we can find our sample size to be 100 and 53. Alright with all this information to let's just start trying to figure some stuff out. The state are no hypothesis in our alternative hypothesis, luckily is already given to us in the sacrum results. So we can see there are no hypothesis is h not. They're saying the sand the variance is equal to 100 and the alternative is our variance Does not equal to 100. So this is a two tailed test. So now let's see if we can find the testes cystic. So for testing the variance, the test statistic Gonna be defined as Chi Square, which is going to be equal to end -1 times the sample variance divided by our there are variants, Recalling -1 is just our degree of freedom. So this is 152 Times are sample variance which is given in the data 128 40-8 to this is all gonna be divided by our variance, which is what are null hypothesis is which is 100. Yeah, This will be approximately equal to 195 17229. Hopefully this number seems you've seen this number already, is this number here was also given in the data, that's the chi square step. So we know the test statistic is 195. Yeah. Um Normally if you have a chi square table or normally you will try once you have this, you look at the chi square table to see if you can find the p value, but normal chi square table only goes up to a degree of freedom. 100 we have a degrees 152. So we're going to use the p value given to us, which is right there. So we know our P value Is 0.0288. Yeah. So what is this P value telling us? So a p value is the probability of obtaining results at least as extremes as is observed results assuming don't know her processes. It's true. So since the critical value, so that is what the P values also since the critical value isn't really given and we have such a large degree of freedom. Normally the critical value for testing the variants would be chi squared degrees of freedom with alpha over to or chi square degrees of freedom, one minus alpha over to. And this goes into with our rejection region. Since this is a to tell tales, you will reject the null hypothesis. If the testes cystic is less than our chi squared Off over 2° of freedom or if our testes cystic was greater than Hi score 1- Off over to our degrees of freedom. Yeah. Again, since we don't we can't really find the critical values since it wasn't given to us and the degrees of freedom is large. We're going to solve this. Come to conclusion based on the p value results. So there's two results we can get is the p value is greater than alpha. We will reject the null hypothesis. Are not rejected. I'm sorry, we will accept the holocaust is if the p value is less than alpha, we will reject. So no hypothesis at that significant level. So recall r p value 0.028. And our alpha. No. Well, in this case are Alpha is 0.05. So we will reject the null hypothesis. So that's we're not a sense the P value Which equals 0.028. Yeah. Is less than alpha which equals 0.05. We will reject. Rh not. So what does that mean in our actual conclusion for this data? So remember, The claim is a normal range of pulse rates among adults is typically given 60-100 beats per minute. The resources are standard deviation equals 10 beats per minute. So we can our conclusion. Sure. Yeah, we can say there is sufficient evidence warrants rejection of the claim. Yeah. That pulse rates of adults have a standard deviation Equal to 100 to 10 beats permanent. Yeah. Mm. So using the rule of thumb, yeah, with normal range of 60 to 100 is not a very good estimate. Our estimate for or estimating Yeah, center deviation in this case.