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Suppaac trat E iinancial aid alots teatbook stipend claiming that the avcraee tcxbook : BC bookicre cona 896 54. You Waut (0 Iest this claim_The null and altenative...

Question

Suppaac trat E iinancial aid alots teatbook stipend claiming that the avcraee tcxbook : BC bookicre cona 896 54. You Waut (0 Iest this claim_The null and altenative hypothesis synnbols would be; Xo;u 93.54 H:e 96.64 Hote <96.54 Hi:e 90.54 0 Ho:P 90.54 Hi:p 96.54 Ho:P Ju.5 Htip 96.54Ho:u 965 Hi:e 96.54Ho:P 96.54 M:P 96.54Thc null hypothesis words Would bc;Thc wcrage pTice of textbooks5 eample i 96.54 Thc avcrage price ofall tcxtbook. froan ttc stonc 96 {4 Tlc proportion of all textbook : from

Suppaac trat E iinancial aid alots teatbook stipend claiming that the avcraee tcxbook : BC bookicre cona 896 54. You Waut (0 Iest this claim_ The null and altenative hypothesis synnbols would be; Xo;u 93.54 H:e 96.64 Hote <96.54 Hi:e 90.54 0 Ho:P 90.54 Hi:p 96.54 Ho:P Ju.5 Htip 96.54 Ho:u 965 Hi:e 96.54 Ho:P 96.54 M:P 96.54 Thc null hypothesis words Would bc; Thc wcrage pTice of textbooks5 eample i 96.54 Thc avcrage price ofall tcxtbook. froan ttc stonc 96 {4 Tlc proportion of all textbook : from tz storc that arc kaa tan 96.54 Eqnl S0 : Tlc #vcragc of pricc ofall tcxtbuoks fot thc slozc kaa tLu $ 96.54. Thc #erage of price ofall extbooka from the #ore ercatet thin 96 $4. Based ou a samplc of 90 textbook s the store. you find ; avetage of 93.74 and standard detiation 0f 15.6- Poinut _ estimate i: decimals) The 99 - confidcnce intcrval (u+2z*) decimals) Bascd thi: wc; Rcjcct thc null hypothcsis Fail = reject the null hypothesis nlnin possible; Lancna



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(a) identify the claim and state $H_{0}$ and $H_{a},(b)$ find the critical value and identify the rejection region, $(c)$ find the test statistic $F,(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. If convenient, use technology. The table shows the salaries of a sample of individuals from six large metropolitan areas. At $\alpha=0.05,$ can you conclude that the mean salary is different in at least one of the areas? (Adapted from U.S. Bureau of Economic Analysis) $$\begin{array}{|l|l|l|l|c|l|}\hline \text { Chicago } & \text { Dallas } & \text { Miami } & \text { Denver } & \text { San Diego } & \text { Seattle } \\\hline 43,581 & 36,524 & 49,357 & 37,790 & 48,370 & 57,678 \\37,731 & 33,709 & 53,207 & 38,970 & 45,470 & 48,043 \\46,831 & 40,209 & 40,557 & 42,990 & 43,920 & 45,943 \\53,031 & 51,704 & 52,357 & 46,290 & 54,670 & 52,543 \\52,551 & 40,909 & 44,907 & 49,565 & 41,770 & 57,418 \\42,131 & 53,259 & 48,757 & 40,390 & & \\& 47,269 & 53,557 & & & \\\hline\end{array}$$

In this problem, we're going to be testing the claim that oxygen treatment is effective for people who have very painful cluster headaches. We have two samples. One sample received oxygen treatment on the other sample received possible treatments, so 150 patients were treated with oxygen, and out of the 150 people, 116 are free from headaches, so the proportion is 116 divided by 115. And for those who are given the possible, you have 29 free from from the headaches 15 minutes of the treatment out off a total of 148 patients. So we're going to test the claim that the oxygen treatment is effective and we're going to use two approaches. The fast approach will be the hypothesis hypothesis test, and the second one will be. The confidence interval meant better now for the hypothesis test method. We're going to have the Nahal hypotheses as P one equals p two, which is to say that the proportions are equal and to prove that them oxygen treatment is effective. It would be that the proportion off those who received oxygen treatment and war free from headaches is greater than the proportion off those who received the placebo. And we're free from, um, headaches. Now we can work out the test statistics by substituting the values we obtained into the formula for that. And when we do so, the calculator value of that is nine point 96 Next, we can get the critical value for this, uh, one tales test at the 0.1 significance level. On the calculated value of that is the critical value of set for that is going to be 2.33 So we can compare the conclusive body of that in the critical money upset. And in this case, we have 2.33 can shape that critical region, and we see that 9.96 is within the critical region. And for that reason we reject the national hypothesis. This'll means that there is sufficient evidence to support the claim that the cure rate with oxygen treatment is higher than the cure it for those given a placebo. So it appears that the oxygen treatment is effective from the hypothesis test. Let's see what happens when we conduct the confidence interval test So for the confidence interval, we need to substitute the value, Uh, the values that we have obtained the into the formula and to get the imagine of error e And when we do so, imagine of error is 0.1101 And when we can also substitute the values, uh, into the expression for the confidence interval you obtained, the interval limits US zero 0.4669 less than p one in a speed too less than 0.6871 And when you look at the intervals at the interval limits, we do not have zero in between. So the internal limits do not include zero, and that means that the two curates are not equal. In other words, we would have to weigh would have to reject the null hypothesis. So this confidence interval test is in agreement with the hypothesis test. And so it appears it appears that the cure it with oxygen treatment is higher than the cure it for those given a placebo, and that means that the oxygen treatment is effective. Next, we're going to to give a reason as's, too, as whether or not the oxygen treatment is effective based on the two tests. So based on the two results the conflict, the hype of the serious test and also the confidence interval test, there's an agreement that there is a difference between those two proportions. So the results. Both results suggest that the oxygen treatment is effective in curing cluster headaches.

In this problem, we're going to be looking at the outcomes off randomized control child in Kenya. Well, insecticide treated bed bucks one tested and the way to reduce malaria. So we're going to be using the European 01 significant level to test the clean that the incidence of malaria is lower for infants using bed nets. So we have two samples. The first sample is made up off the infants who used bed nets and the second sample hard influence who did not use business. So for those who used bed nets, 15 in France got malaria out off 343. And for the infants who are not using bed nets, 27 got malaria out off 294. So you're going to be testing the claim that the incidence of malaria is lower for infants using bed nets, using the hypothesis test method and also using the confidence interphone method. And then after that, we're going to compare the results until whether bed nets appear to be effective. So for the test of hypothesis test, we're going to used the level of significance zero from 01 on the night hypothesis. Use P one is equal to P two, and the alternative hypothesis he is P one. It's less than picture. So this means that the proportion off Indonesia when they had bed nets is lower than the proportion off infants who got malaria when they had no bed nets. Therefore, the critical Valley for this will be mhm negative 2.33 And now we need to work out the value of the test statistic, and in this case we have to substitute the values accordingly. And when we do that, the value upset, it's negative 2.43 So now we can compare their valleys upset. And in this one tailed test, critical value is negative 2.33 Can she eat that? You find that they just statistic is owned the left hand side, which is within the critical region and for that reason, and make the conclusion to reject the non hypothesis. So by rejecting the Nalle hypothesis, we conclude that there is sufficient evidence support the claim that the incidence of malaria is lower for infants using bed nets because it appears as if the proportion off students off infants who got malaria when they had bed nets is much lower than the one off in France. He caught malaria when they have no business. So now we need to compare them. Yeah, the two tests the confidence interval test and they have other sisters. Well, let's go through the confidence interval teachers and the confidence interval test. We need to work out the margin of error e substitutes in the violence accordingly. And when we do that, we get e zero point. It's usual 47 and when we substitute the value to the expression that gives us the confidence interval, he said that they're lower limit his negative zero point. It's usual 95 Well, the upper limit is negative 0.1 So all the values here are negative and confidence interval interval limits do not include zero. Therefore, it appears that the two proportions are not equal, and because the confidence intervals includes only negative values, it appears that the proportion off infants who got malaria when they had bed nets is much lower than the proportion off infants who got malaria when they had no bed nets. So based on the results, it appears as if bed nets are effective in reducing by liberal transmissions amongst infants

In this problem, we're going to be testing the effectiveness off. ECON ASIA In treating calls, we have two groups off subjects. The first subject was given a kidney Asia. The first group was given magnesia, and the second group was given a placebo. So we can say P one hunt represents the proportion off the people who developed the retrovirus infections after being given a condition, and that is 40 45. So that's a fraction off. Those who developed renew various infections after being given akin Asia. And for those who developed in various infections after being given the possible are 88 out off a total of 103 subjects. And to test the effectiveness off back in Asia for Coles, we're going to use two approaches. The fast approach is going to be a hypothesis. Test on the second one is going to be the confidence interval. So we're going to use the 0.5 significance level, and we're testing the clean that back in Asia has an effect on rhinovirus infections. We're not giving, uh, we're not saying that one has ah, one is more effective than they ever were. Just saying that there is no effect on grain of virus infections that makes these tests are two tails test on the critical value on that is plus or minus 1.96 So let's go ahead and get the test statistic, which is that obtained by substituting the values obtained into the formula. And when we do so, we get the calculated value of that zero point 573 and when we compare the calculated value of that and the critical value of that in this case we have it as 1.96 positive and negative 1.96 So the calculated value of that is zero 0.573 and it is not within the critical region and for that reason we fail to reject the narrow hypothesis. Failure to reject an al hypotheses means that there is not sufficient evidence to support the claim that back in Asia has a NIF effect. So we move on to the second test by constructing an appropriate confidence interval and to do so to get a 95% confidence interval. We need to use the formula given and fast work out the margin of error e, and when you substitute the values off into the formula, we get that. The margin of error e is 0.1143 and when we substitute this into their confidence interval, we get that. The intervals limits are negative. 0.7 93 less than P 1 may not be too, and 0.1493 So we noticed that the confidence interval limits do contain zero, so zero is included within the confidence interval limits and thes shows that there is not significance thing. There is not a significant difference between the two proportions because when zero is included, WAY can see that there is not a significant difference between the proportions. In other words, there is no sufficient evidence to support the claim that back in Asia treatments has an effect. And in the last part of the question see, we're answering the question. Does echinacea appear to have any effect on the infection rate and according to the results, we see that back in Asia does not appear to have a significant effect on the infection rate and because it does not appear to have an effect, a significant effect, it should not be recommended because it's a safe for those two proportions do not have any significant difference.

Hi. We're gonna start with stating our null hypothesis, which happens to be a mule or the mean is equal to 15 1000 on our claim. And alternative is you'll is not equal to 1500. And as you know this Ah, here we have another equal science off means we are And, uh, two pails case, So just be aware of that on the critical value is equal to minus 2.2 secs because we have any equal to 10. So degree of freedom is nine. Andi Alfa is born or five on. You can find it either in table or software. I haven't toe shoes. Microsoft excel for you on to use statistics. Here is, um the average minus mule divided by it's over square depend on the answer is minus one when all seven and also I used Microsoft excel to compute everything so we cannot reject the notes. Is this value is not listening and I'm gonna show you graphically. What does that mean? Uh, let me summarize. That is also there is no evidence that the average is 15,000. I assume this our distribution. So I want critical values here and our minus physical value is here. So the addiction area is either here or here. But we haven't. We have our dispel you some where? Here. So we are not in rejection A


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