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To test the hypothesis that the population standard deviation sigma-18.9, sample size n-11 yields sample standard deviation 14.701_Calculate the P-value and choose ...

Question

To test the hypothesis that the population standard deviation sigma-18.9, sample size n-11 yields sample standard deviation 14.701_Calculate the P-value and choose the correctconclusionYanitiniz:The P-value 0.015 is not significant and s0 does not strongly suggest that sigma<18.9. The P-value 0.015 is significant and so strongly suggests that sigma<18.9. The P-value 0.002 is not significant and so does not strongly suggest that sigma<18.9. The P-value 0.002 significant and so strongly s

To test the hypothesis that the population standard deviation sigma-18.9, sample size n-11 yields sample standard deviation 14.701_ Calculate the P-value and choose the correct conclusion Yanitiniz: The P-value 0.015 is not significant and s0 does not strongly suggest that sigma<18.9. The P-value 0.015 is significant and so strongly suggests that sigma<18.9. The P-value 0.002 is not significant and so does not strongly suggest that sigma<18.9. The P-value 0.002 significant and so strongly suggests that sigma<18.9. The P-value 0.346 is not significant and s0 does not strongly suggest that sigma<18.9. The P-value 0.346 is significant and so strongly suggests that sigma<18.9. The P-value 0.189 is not significant and so does not strongly suggest that sigma<18.9. The P-value 0.189 is significant and so strongly suggests that sigma<18.9. The P-value 0.008 is not significant = and does not strongly suggest that sigma<18.9. The P-value 0.008 is significant and so strongly suggests that sigma<18.9.



Answers

ILLUSTRATE the use of the sign test to test hypotheses regarding a population proportion. The only requirement for the sign test is that our sample be obtained randomly. When dealing with nominal data, we can identify a characteristic of interest and then determine whether each individual in the sample possesses this characteristic. Under the null hypothesis in the sign test, we expect that half of the data will result in minus signs and half in plus signs. If we let a plus sign indicate the presence of the characteristic (and a minus sign indicate the absence), we expect half of our sample to possess the characteristic while the other half will not. Letting $p$ represent the proportion of the population that possesses the characteristic, our null hypothesis will be $H_{0}: p=0.5 .$ Use the sign test for Problems 17 and $18,$ following the sign convention indicated previously.
In a study of 2302 U.S. adults surveyed online by Harris Interactive 1243 respondents indicated that they tend to not trust the press. Using an $\alpha=0.05$ level of significance, does this indicate that more than half of U.S. adults tend to not trust the press?

Okay, so in this question, were given that X is equal to 6062 on physical too. Okay, 5938. Plus, that's 6062 which will equal to 12,000. We're else given. P is your five on Alfa are those significance is your is your five all right? Okay, so now we can calculate our proportion, which is X over end, which is 6060 to over 12 passion, which is equal to 0.50 52 Yeah, it's now the hypothesis is given by it's not to know that, but says P is your five that alternative hypothesis H A P is less than 2.5. Okay, Now can calculate our Z test statistic, which is question might be cover squared. Q p off on a kid, thank you is equal 21 nice people. P is your for five. Yeah, So if you plug all these values and we'll get a Z value of 1.14 and to now you can get our critical values. So z half a is equal to negative 1.645 from the table that is our C critical value Andi R P value, which is just the p probability that g less than 1.14 which is just equal, does your point is 7 to 9 on. Since this is greater than our critical value, which is 0.5 you can fail to reject our no hypothesis h not.

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.

All right. We are observing a population with mean 4.8 and we want to calculate the sample mean and standard deviation for the following sample data obtain to do this. We we know the definition of expire and S for a sample which are given here, X is equal to some of the data divided by n or 4.4, and s is equal to the sum of the deviations about the mean square, divided by n minus one or 0.28 Next we want to implement a left tailed test on this particular population, so we want to test the population is actually less than 4.8. Using a significance level output equals 0.5 Where we are told that X is approximately normal, that is this distribution is approximately normal. So we have to answer the following questions. In order to complete this test. To start off with, what are the significance of hypotheses? Alpha equals 0.5 No hypothesis H is new at this 0.4 point eight and H. A. Is that me was less than 4.8. It's the left tail test. What distribution When we used to be the test statistic, we're going to use a student's T distribution because sigma is unknown. We know that we can do so because the shape is symmetrical and bell curved. Given this, we want to calculate the T stat which is given by this formula. The T stat here equates a negative 3.499 Now, given this T stat, we want to compute the P P interval and then sketch the associated students distribution for P. Since we have degree of freedom, uh six minus one equals five. We have the R. P interval is between 50.5 point 01 We can grasp this as the area to the left of our T stat highlighted here in yellow and Marcus P. From this, we can conclude since P is less than legal to alpha, we have statistically significant findings and we can reject R. H. Saw, which we can interpret to ultimately mean that we have sufficient evidence suggesting our population means is less than no means for pointing.

Right, where will the population has mean new equals 14 From the following sample data, we want to calculate the sample mean X bar and the sample standard deviation S. To do so let's remember the definition of these terms X bar Is the some of the data divided by n or in this case 15.1, I'm a sample standard deviation S is the sum of deviations about the mean square divided by n minus one or 2.51 Next we want to implement a right tail test. That is we want to test whether or not the population mean should actually be greater than the no mean 14. With us using the sample data with a significance level alpha equals 140.1 Where we are noted that X is approximately normally distributed. So to implement this test, we have to answer the following questions in order First, what is the significance of hypotheses? We've alpha equals 0.1 H not is new equals 14 H. A. Is that I mean is greater than 14. What distribution will use computer associated test statistic? Since the population standard deviation sigma is unknown. We have to use a student's T distribution which we know is okay to use because the shape of the distribution is normal, which is both symmetrical amount shaped from this. We calculate the T stat Which is given by this formula and reduces down to 1.386 for this problem? Next compute the p interval and sketch it out so we have degree of freedom and minus 29. We use the one tailed T. Table to identify that this tea interval falls between a p interval of 10.75 point one. That is because our T statistic falls between associated T values for these p values. We can graph this as the area under the student's t distribution. To the right of our T stat 1.386 as is highlighted in yellow on the right. What can we conclude from this? Well, we can conclude that P is greater than alpha, so we have statistically insignificant findings and we fail to reject astronaut, which means that we lack sufficient evidence that suggests our population mean is greater than the No. Mean 14.


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