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Trials in an experiment with a polygraph include 9999 results that include 2424 cases of wrong results Use a 0.05 significance level to test the claim that such pol...

Question

Trials in an experiment with a polygraph include 9999 results that include 2424 cases of wrong results Use a 0.05 significance level to test the claim that such polygraph results are incorrect more than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, p-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim Show all calculations that lead to your results:

Trials in an experiment with a polygraph include 9999 results that include 2424 cases of wrong results Use a 0.05 significance level to test the claim that such polygraph results are incorrect more than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, p-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim Show all calculations that lead to your results:



Answers

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Trials in an experiment with a polygraph yield 98 results that include 24 cases of wrong results and 74 cases of correct results (based on data from experiments conducted by researchers Charles R. Honts of Boise State University and Gordon H. Barland of the Department of Defense Polygraph Institute). Use a 0.05 significance level to test the claim that such polygraph results are correct less than $80 \%$ of the time. Based on the results, should polygraph test results be prohibited as evidence in trials?

So we're given that an is equal to 300. Alfa is equal to 0.5 Mm yeah, which is our level. Significance on X is equal to 27. Therefore we can kill. Okay, X over n which is equal to 27. Okay, 300 literally. Call. Does your point. Zero? No. So, Donald, Hypothesis H nine is a P is equal to 01 andare alternative hypothesis is a P is less thens you're going so we can now use our formula to find those eat statistic. Yes. Yeah. Square P time zone minus p over. And which is he called? 009 minus zero. Mhm. Over the square was your one Times one nice. You should you. And over 300. She'll give us natives Europe 58 Now we can find g critical value, which is equal to negative 1.645 She was in our value. If she opens your Fife. Andi since r p value a z less than two negatives Europe on the side eight, which is equal to 0.280 man. Okay, it's there for the p value is greater than yeah, pretty cool significance level and therefore you can fail to reject the age, not there is not enough evidence to conclude that the proportion of test, which are wrong, is less than 10%.

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 comparing the accuracy off fast food drive thru orders for two restaurant chains. We have two samples, one from Burger King and one from McDonald's and for Bank Akin, 54 out off 318. Orders are accurate, so the proportion is 54 often 318 for McDonald's. We have 33 accurate orders out off 362 which is the proportion off accurate orders for McDonald's. So in this problem, we shall be testing the clean that Burger King and McDonald's have the same accuracy rates, and we'll do so using two approaches. The fast approaches the hypothesis test method. On the second approach is the confidence interval method. So afterwards we're going to discuss which off the restaurant chain's appears to be better relative to accuracy off orders. So let's begin with a hypothesis test, and for this, we're going to be using the 0.5 level of significance bond. Now hypothesis is P one equals P two, which is to say that the two proportions are equal on the alternative hypotheses will be. P one is not equal to P two because according to the clean, we have to check that Burger King and McDonald's have the same accuracy rates, so this will be a total test. Therefore, critical value for Zet is plus or minus 1.96 So we now need to work out the value of the test, Statistics said. By substituting values into the formula has required and when we do so, they concluded. One of that is 3.7 uh, seven. Yes, and now we can compare the test statistic and the critical value and in this case, critical region, he's she did. So this is positive. 1.96 This is negative 1.96 and the test statistic is within the critical region. And for that reason you make the decision to reject the national hypothesis, each not. And by rejecting the null hypothesis hitch knot, we conclude that that is not sufficient evidence to support the claim that bag a king and McDonald's have the same accuracy rates. Now we can move on to the next method, which is the confidence interval method, and here we need to conclude the era off margin. The margin of error using the formula given we're substituting the values accordingly and when we do so, the value off e is going to be zero point zero 508 and when we also substitute the value off e into the expression that gives the confidence interval, we see that the lower limit for the confidence interval is zero from zero 282 on the upper limit is 0.12 98 and we noticed that the confidence interval does not contain zero. And when the confidence interval does not contain zero, it shows that the two proportions have different values. So in the party of the question, we can tell whether which we can tell which off. The restaurant chain appears to be better relative to accuracy off orders. And when we compare the two proportions, we see that fourth Burger King. 17% of the orders are accurate, while for McDonald's, 9.1% of the orders are accurate. And since there is a significant difference between the two of proportions, one can conclude that bag a king has better accuracy rates compared to McDonalds

Were given that significance level. Alfa is equal to zero point. You're one. And people who have pulled in favor can be represented by X, which is equal to 481 on the people who opposed is 401. So we get the total number of people this 401 plus 481 physical to 100. You need to Okay, okay, on the given claim is equal to zero point five. Sure. Yeah. Okay, So the claim is that either the null hypothesis or alternative high boxes state the opposite each other on the null hypothesis needs to contain the value mentioned claim. Okay, so you know that the null hypothesis is P is equal to 05 Walter type boxes is just a P is not you. Does your there for the sample proportion, which is the number of successes divided by sample size is equal to X over and X number of successes on. And there's a number simple slips So to your 481 of 382 which is approximately equal to 0.54 54 now, if to determine value of the test statistics of Z is equal to p. There is pure not or the square root of P not times one minus over. And so therefore, if you're plugging all the values since Europe 5454 here minus peanut which is 050 divided by the square root off June 5 times one might in Super five, which is a stupid can over 882 which is equal to 2.7. It's you. So now the P value is the probability of obtaining the value of the test statistic or value more extreme. When the hypothesis is true, you have to to determine the value of P using the normal probability table. Okay, on the former P is equal to P or C was negative. 2.7. Yeah, where is he? Greater than 2.7, which is equal to two p. See Destiny 2.7, which will give us a final answer of two times your point shoes. You 35 which is Joe could choose your shit. Sure. Okay, so now, since this P value is less than our, um, significant level Alfa, we can reject the null hypothesis because PVA is less than significance lovely. Therefore there is sufficient evidence to reject the claim that the proportion of subjects responded in favor is equal to 0.5 and therefore the politicians claim is false.


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