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Test the claim that the proportion of men who own cats smaller than the proportian of women who own cats at the .05 signilicance evel:The null and alternative hypot...

Question

Test the claim that the proportion of men who own cats smaller than the proportian of women who own cats at the .05 signilicance evel:The null and alternative hypothesis would beHo: PM PF Ho: #M #F Ho : PM PF Ho; PM Ho : #M ELF Ho: UM Ki:PM > PF H:pM + #F H:pM # PP H:pM PF H:eM #FH KMThe test i5;two-(ailed right-tailed Ieft-tallledBased on sample of 80 men; 3540 owned cats Based on sample of 80 women 609 owned cJtsThe test statistic297decimals)The p-value0,01decimals)Based on this we:R

Test the claim that the proportion of men who own cats smaller than the proportian of women who own cats at the .05 signilicance evel: The null and alternative hypothesis would be Ho: PM PF Ho: #M #F Ho : PM PF Ho; PM Ho : #M ELF Ho: UM Ki:PM > PF H:pM + #F H:pM # PP H:pM PF H:eM #FH KM The test i5; two-(ailed right-tailed Ieft-tallled Based on sample of 80 men; 3540 owned cats Based on sample of 80 women 609 owned cJts The test statistic 297 decimals) The p-value 0,01 decimals) Based on this we: Reject the null hypothesis 0 Fail to reject the null hypothesis Question Help: DMessage instructor 0 Post fotum Sunmi Questiom



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. Assume that a simple random sample is selected from a normally distributed population. Spoken Words Couples were recruited for a study of how many words people speak in a day. A random sample of 56 males resulted in a mean of 16,576 words and a standard deviation of 7871 words. Use a 0.01 significance level to test the claim that males have a standard deviation that is greater than the standard deviation of 7460 words for females (based on Data Set 24 "Word Counts").

So the objective is the test to claim that 51 0.2% of newborn babies or boys So let P be the proportion off newborn babies there, boys. Therefore, we confined our hypothesis, which is your 0.5120 on our alternative hypothesis, which is the P is not equal, right? Did you have been fine? Two's your and let the level of significance Alfa P equals 0.4 Okay, so now we know that the number of births in the sample is 160. The number of newborn babies there, boys is you got to for 26 2 different example. Proportion of newborn babies, daughter boys, this will be had is equal to X for her end, which is equal to 426 over 160 which is equal to 0.4 95 Okay, now the Z test statistic he Yeah, school of peak over and cute is equal to one Manus people on p European five tissue. So if you just go ahead and plug these values and P and bullshit, we will get as he the statistic of negatives. You 0.9 eight So now, from the alternative hypothesis, it is clear that the test is two tailed on the standard normal table. At 5% level of significance, you can find the two tailed critical value to B C off to 1.96 Therefore, that is a critical value off plus or minus six, and you're the value of the test statistic is negative 0.98 which is greater than the critical value of negative 1.96 So therefore we can fail to reject the hypothesis and conclude that the proportion of newborn babies are 51.2%.

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

Okay, so we know that the null hypothesis h not is that p is equal to 0.75 on alternative hypothesis is that p is greater than the European 75 Okay, So to find the test statistic, we're gonna find pushing p. No, but says screw off peak, you ends. My cute is one minus p andi way. We know also from the question on 3000 five on DSO can calculate our Z value to be 8.48 Okay? By substituting all the values we are given. Okay. All right. So now the P value is equal to 0.0 She's lessons. European Ship one Therefore we can reject. Don't know. Hypothesis sentence. This is our critical.

In this problem, we're going to be testing the claim that the writ off left handedness among meals ISS less than that among females. And so we have two groups. Two samples and way have 240 males and 520 females. So out of the 240 males, 23 are left handed. So the proportion off left handed meals is 23 out of 240. And for the left 100 females, the proportion is 65 out of 520. And for this, uh, for this testing, we're going to use two approaches. The funds approaches the hypothesis test on the second approaches the confidence interval method and for the help. But this is test. We're going to use the 0.1 significant slept And since we are testing the clean that, uh, the rate off left handedness among males iss less than that among females, the now hypotheses will be P one is equal to p two. On the alternative hypotheses will be P one IHS less than p two, which means that the proportion off meals see meal is smaller than the proportion for females. And for that reason the critical value will be negative 2.33 Because this time we're saying that the proportion ISS less so since it's less the proportion of male is less than pushing off female. We use the negative, um, part off the pictographs. So negative 2.33 So now we want to get the calculated value of that. And to do so, we have substitute the values that we have here in the formula, and we obtain the value of that as negative 1.1 six. So now we can compare the critical value of that and the calculated value of that. So in this case, we see the critical region is the region to the left off negative 2.33 and the completed value of that He is not within the critical region. Uh, because negative 1.16 is to the right off the critical value. So this means that we'll have to make the conclusion to fail to reject denial hypothesis, which means that there is not sufficient evidence to support the claim that the writ off left handedness among males iss less than that among females. Now let's see how the the results would be for confidence interval test. So to test the claim, we would have to work out the value off e by substituting the values they into the formula. That is, the margin of error on the margin of error is 0.557 when you could substitute all the values correctly and also when you substitute the values correctly into this expression for the confidence interval, the thing you notice that the interval limits are negative. 0.8 47 Aunt Positive 0.267 So those are the confidence interval limits and this tells us that the difference between the proportions contains the difference. The confidence interval for this difference contains zero. It includes zero on this means that there does not appear to be a significant difference between the rich off left handedness, uh, among meals Andi riddle among females. Okay, so that doesn't appear to be a difference. And thanks. In other words, there is not sufficient evidence to support the claim that the rate off left handedness among males iss less than that among females. So in the last part of the question patsy. We're going to be using the results from the tool tests to tell if the writ of left handedness among males uh, it's less than the rich off left handedness among females. And we see that the two tests are in agreement that the rate of left handedness among this does not appear to be less than the rate off left handedness among females. Because we rejected the not we fail to reject the null hypotheses. Uh, then we can conclude that that does not appear to be any difference between the 22 categories the males and the females.


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