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13. I You rejct the null hypothests for a hypothesis lest; which of the 'following are truc? Wc may have observed an extrcmely rare ocurrence, Wc may have comm...

Question

13. I You rejct the null hypothests for a hypothesis lest; which of the 'following are truc? Wc may have observed an extrcmely rare ocurrence, Wc may have commilted TType crror We do not believe the null hypothesls is reasonabloIl only(b) Hand II only and Ilonly (d) I,and IIISuplse Vou conduct signilleanca !ont Ioor Uhe ppulatlon Mewn; Ad your P-value Is,30 At the 5" signulicarv devcl, You nhoukl (4) Rcjre( Ho Fail to rejeel Ha Acccpt Ha (d) Accvpt HeSupi"ose Men lestingF Ha 47 10

13. I You rejct the null hypothests for a hypothesis lest; which of the 'following are truc? Wc may have observed an extrcmely rare ocurrence, Wc may have commilted TType crror We do not believe the null hypothesls is reasonablo Il only (b) Hand II only and Ilonly (d) I,and III Suplse Vou conduct signilleanca !ont Ioor Uhe ppulatlon Mewn; Ad your P-value Is,30 At the 5" signulicarv devcl, You nhoukl (4) Rcjre( Ho Fail to rejeel Ha Acccpt Ha (d) Accvpt He Supi"ose Men lesting F Ha 47 10 Wlue d Uv: Uaz Ad Ilu Ivsull Mu vuawuld



Answers

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis.
State the null hypothesis, Ho, and the hypothesis. $H_{a},$ in terms of the appropriate parameter $(\mu \text { or } p)$
a. The mean number of years Americans work before retiring is $34 .$
b. At most 60$\%$ of Americans vote in presidential elections.
c. The mean starting salary for San Jose State University graduates is at least $\$ 100,000$ per year.
d. Twenty-nine percent of high school seniors get drunk each month.
e. Fewer than 5 $\%$ of adults ride the bus to work in Los Angeles.
f. The mean number of cars a person owns in her lifetime is not more than ten.
g. About half of Americans prefer to live away from cities, given the choice.
h. Europeans have a mean paid vacation each year of six weeks.
i. The chance of developing breast cancer is under 11$\%$ for women.
j. Private universities' mean tuition cost is more than $\$ 20,000$ per year.

In this problem, we're going to be testing the clean that the survival rates for patients who had cardiac arrest during the the D. Waas the same uh huh, for patients who had carried cardiac arrest at night. So we have two samples way. Have patients who got cardiac arrests. That's not during the day and the proportion off those who survived. He's 1 11,000 604 our tooth 58,000 593. So that's the proportion for patients who survived. You survived during the day, and that's night. The proportion of patients who survived waas 4000 139 out off 28,000 155 So we're testing the clean that the survival rates are the same for day and night. So we're going to do that using the hypothesis test method and using the confidence interval method. So the level of significance Alfa it's 0.1 on the non hypothesis he is P one is equal to P two alternative policies. His P one is not equal to be to, and for that reason, the critical value for Zet he is classroom minus 2.5 seven. So now we can walk out the test statistics and substituting the values into the formula. And when you do that, the calculated values that is 18 point 27 and when we compare that to the critical value, you'll notice that the value 18 is within the critical region. That's 18.27 So since it's within the critical region, we make the conclusion to reject the non hypothesis and when rejected an hypothesis, we conclude that there is not sufficient evidence to support the claim that the survival rates are the same for day and night. Now we move on to the second approach, which is the confidence interval method, and here we work out the value of the margin of error by substituting the values into the formula. And when we do that, we get that e is zero point 00 69 on the confidence interval limits are 0.0 441 and 0.0 five 79 So according to the confidence inter form, the confidence interval limits do not include zero. So since they did not include zero, it appears that the two proportions are not equal because the confidence interval limits include Onley positive values. It appears that they read off survival during the day is different from that at night and therefore it is it is in agreement with the fast test name for this is test. So based on the results, were supposed to tell when it appears that for in house or in hospital patients who have a cardiac arrest, the survival rate is the same for day and night. And since we rejected another hypotheses, we see that one of these writs is much greater than the other, and when we give the percentage off survival during the day, the percentage is 19 8% and at night the percentage is 14.7%. So this since there's a significant difference between the two proportions, then we can conclude that the survival rates are much better during the day compared to the night

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.

In this problem, we're going to be testing the claim that men and women have equal success in challenging calls from made by the referees in the U. S. Open and the year 2006 10 x. So we have two samples. One sample is made up off 2441 men, and the second sample is made up of 1273 women. So the proportion off calls that were overturned for men is 1000 27. Oh, well, 2441 and the proportion for women's called the schools that Robert turned was 509. What? 1273. And to to test the claim that men and women have equal success in challenging calls we're going to uh huh used to approaches the hypothesis test on the confidence interval medal. So when they have prosthesis test, we're going to use the critical the Significance Level album off 0.5 And in this case, the null hypothesis is p one equals Sorry. P one is equal to P two. On the alternative hypothesis, his P one is not equal two p two Therefore, this is going to be a two tails test and the critical value for that is plus or minus 1.96 And therefore we now need to work out the values, the critical value theory, test statistic, that value by substituting the values. Okay, so when we substitute and values correctly, the value off zed clear value of that he is 1.23 three, so we can compare the critical value on the completed value said, drawing the critical regions. Here we have the critical region and when we look it test statistic, we notice that it is not within the critical region and for that reason we fail to reject. I'm not hypothesis. When we fail to reject the non hypotheses, it means that there is enough evidence there's sufficient evidence to support the clean that the men and women have equal success in challenging the colts. So, in other words, the proportions don't seem to have any significant difference between them Now. When we compare when you test using the confidence interval method, then we need to substitute the values in the formula for getting e correctly on. When we do that, we get E 0.0 333 and for the confidence interval limits, the lower limits is negative. 00 123 yeah, and upper limit 0.5 43 And this confidence is have one includes zero, which means that there does not appear to be a significant difference between the proportion off men. Men's caused men's calls that get overturned, the proportion off women's cause that get overturned. So this is in agreement with hypothesis test that shows that there is not enough There's enough stuff. They sufficient evidence to support the claim that the men and women have equal success in challenging counts. So, patsy, the question requires us to to tell whether it appears that men on women have equal success in challenging the Colts. Based on the results, we see that both men, and even appear to have the same proportions off course that are off a ton

In this problem, we're going to be checking whether, as spring prevents, heart disease, and we're going to be using the outcomes from a child made on to two samples. The first sample was made on 11,000 37 male physicians will receive aspirin and 11,034 main pre physicians who is were given placebos. So the proportion off subjects in the aspirin treatment who experienced heart attacks are is 139 out of a total off 11,000 that is, have the proportion off male subjects in the placebo group. As you see, that experience had attacks was 239 out off 11,000 34. So we'll be testing the clean that aspirin has no effect on heart attacks. So we're using the hypothesis test method on also the confidence interval method. So the leg level of significance often is 0.5 On the hypothesis, R P p one equals P two for the null hypothesis on For the alternative hypothesis, P one is not equal to P two, so this is going to be a two tailed test and therefore the critical value said he is plus or minus 1.96 So we can work on the test statistics that by substituting the values accordingly and when we do that, we get negative 5.171 so we can compare. That is calculated value of that, the critical finally, that as well during the critical region. So we have 1.96 negative, 1.96 So negative 5.17 falls to the left off negative 1.96 And hence it belongs to the critical region. And that leads to the conclusion to reject the non hypothesis. And by rejecting the non hypothesis, we conclude that there is not sufficient evidence to support the clean that aspirin has no effect on heart, a touch disease or heart attacks. Now you can do the same test, but using the confidence interval Meggett and this time we need to substitute the values off into the formula cutting me and the value uh, value off E is going to be zero 0.0 035 They create the confidence interval limits are negative. Zero point 0125 and negative 0.55 So we're not here that the confidence interval does not include zero. And so it appears that the two proportions are not equal. So the because the confidence interval and limits include Onley negative values. Then it appears that the yeah, that the proportion off patients who got the aspirin treatment is much smaller then the proportion off subjects god, placebos and therefore, based on these results, it appears that aspirin is effective in preventing heart disease.


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