4

Last year, 50% of MNM, Inc: employees were female_ It is believed that there has been reduction in the percentage of females in the company: This year _ of 400 empl...

Question

Last year, 50% of MNM, Inc: employees were female_ It is believed that there has been reduction in the percentage of females in the company: This year _ of 400 employees, 180 were femal random sampleGive the null and the alternative hypotheses. 95% confidence using the critical value approach, determine if there has been significant reduction in the proportion of females_ Show that the p-value approach results in the same conclusion as that of Part b

Last year, 50% of MNM, Inc: employees were female_ It is believed that there has been reduction in the percentage of females in the company: This year _ of 400 employees, 180 were femal random sample Give the null and the alternative hypotheses. 95% confidence using the critical value approach, determine if there has been significant reduction in the proportion of females_ Show that the p-value approach results in the same conclusion as that of Part b



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.
Since the Hawk-Eye instant replay system for tennis was introduced at the U.S. Open in $2006,$ men challenged 2441 referee calls, with the result that 1027 of the calls were overturned. Women challenged 1273 referee calls, and 509 of the calls were overturned. We want to use a 0.05 significance level to test the claim that men and women have equal success in challenging calls. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Based on the results, does it appear that men and women have equal success in challenging calls?

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.

Yeah. All right. So, we were given some information about birth weights, birth weights example, random sample of 30 girls have a standard deviation of 829.5 HD. And there's a claim that birth weights of girls have the same standard deviation as birth weights of boys, which is 660.2 is G. And once you use alpha equals 0.01 we will identify the null hypothesis. The alternative hypothesis. The testes cystic, the p values and the critical values or the critical values. Make conclusions about the null hypothesis. And what does that mean for our claim? So, first listen, and find the null hypothesis. We're talking about standard deviation. So it's gonna be sigma And we're claiming that they are the same as the boys, which is 660.2. The alternative Is that well, the waste of the girls do not equal the waste of the voice or the standard deviation. So sigma does not equal 660.2. So, note, we are used doing a two tailed tests. Yeah. So now that we know are no alternative hypothesis, let us find the testes statistic for the testis cyst IX, Since we're assessing standard deviation is going to be a chi squared And the death statistic is N -1 times squared divided by sigma squared. So, looking at our information, we know we have 30 girls are and is 30, So we have 30 -1 -1 S squared is going to be the standard deviation from the girls, which is 829.5 squared. Yeah. And the standard deviation is going to be the standard deviation given the null hypothesis of 660.2 squared? Yes, if we were And this should give you approximately equal to 45 point 78. Mhm. So that's our PVA So that's our test statistics next to find our P value. If we're trying to use the table method. Mhm. The first thing we want to we need fire degrees of freedom, Which again is in -1. So in this case 30 -1 is 29. Yeah, we can find us in the table. So we're it won't give us an exact number For the chi squared but if we go down to 29° of freedom, we're trying to find Between what two alpha values, 45.78 falls under and that will fall under 0.0 25. Saint alpha. Less than 0.1 I think of those science the wrong way. Yeah, but remember, this is a two tailed tests. So when we're dealing with to tell test, once we find where Alfa falls under, we're gonna multiply both sides by two. So this is actually a 0.05 rather than Alpha, which is greater than 0.02. So what we know from the table is that our alpha value falls between 0.05 and 0.02. We don't know the exact alpha though. If you want to get more accurate number for R. P value or far p value we can use our again for our since this is a two tailed tests we're gonna have to have To so this would be two times Yeah P chi square. So the peak i squared is telling us the probability for the sky square, where on what our testes, cystic. So 45.78. This is from our chi square test. The degrees of freedom, Which in our case is for 29. This is our degrees of freedom and there's one more argument which is lower dot tail. This is going equal to false. If it's a lower tail test then this will equal true. True. It is the right tail is equal force and its two tails you want equal to force. And we will multiply this by two. So if you were to put this into our you have to times the p squared. So normally this would be 0.02467139. When you multiply that by two you got 0.04 93 4 to 78. So this is a more accurate reading of R. P value which again agrees those should be P let's just call it p value R. P values between those and this agrees with what we had before this p value is in between these two numbers. So now we can make our conclusions were going to use conclusions based on the p value in alpha. So remember if the p value is greater than alpha, we will accept don't know hypothesis. And if P value less than alpha, we will reject the null hypothesis. Yeah. So here we have a P value of 0.049, and we're using an alpha value of 0.01. So since the P value, Which equals 0.049 Is greater than our alpha, which is 0.01, we fail to reject no hypothesis. So, what that means for our claim, if we go back up to the claim. So since we fail to reject the normal policies, we the birth weight of girls have the same standard deviations as birth weights of voice, which is the 660.2 at a significant level of 1%.

The following is a solution for # 14. This looks at if there's a difference or if men are more often left handed than women. So they sampled 100 and 68 men and 24 of them were left handed and then they sampled 152 women and they found that nine were left handed. So first let's find the point estimate. The point estimate for P one minus P two is simply P one hat minus P two hats. So we just look at the statistics here. So P one hat, let's just say that this is for males is 20 since that's listed 1st 24/1 68 and you get a long decimal, I'm just going around here but 680.143 and then P two hat is for females. So that's 9/1 52. And whenever you plug that in it should be a point oh 59. So the point estimate would be 590.0.143 minus 0.59. Now on this paper I'm rounding but In my calculator actually did. And so I'm actually gonna go to four decimal places here. It's .08 36. So that's my point estimate for the difference of two population proportions. So now I'm going to find the 95% confidence interval if you go to stat and then air over two tests we're going to go to to prop Z. Ent for interval to proportions the interval. So here you can see my data, 24 out of 1 68 for males nine out of 152 for females The confidence levels 95%. And then we calculate so .01878 and .14851. Okay so let's go in Drop that down. So it's between zero 01878. All the way up. 2.14 851. Okay next up we do a hypothesis test the null hypothesis being. There is no difference between men and women and left handedness. And the alternative it says is there a uh is it that the men are there are more men? The proportion of men is higher than women's. That's why P one minus two P two is greater than zero. We're testing at the five percent level of significance. So really all we need is a test statistic and then I'm gonna go ahead and find the people. I'm going to go to the p value out just because that's what this um part DCs so kind of killing two birds with one stone. Especially because I can use a calculator here. So if I go to Staten tests and I go to the to prop Z. Test here you can see that the data is already pre populated and I just need to change this alternative hypothesis. So P one is greater than P two or P one minus P two is greater than zero. And we calculate and my test statistic is 2.457. And that P values quite small so double oh seven there Not the James Bond kind, so z value is 24 57 and then 0.7 which is less than alpha. Now, whenever the P values less than alpha, we're going to reject H. Knock so will reject the null hypothesis and no hypothesis says that there is no difference. So we're accepting that the alternative is true. So it does appear that men are um left handed more often than women and then part D. Says find the P value and I just found it there so 0.0.


Similar Solved Questions

5 answers
Use the given zero to find the remaining zeros of the function. h(x) =x 9x 15x2 93x 700 zero: 3-4iEnter the remaining zeros of h(Use a comma t0 separate answers as needed: )
Use the given zero to find the remaining zeros of the function. h(x) =x 9x 15x2 93x 700 zero: 3-4i Enter the remaining zeros of h (Use a comma t0 separate answers as needed: )...
5 answers
The Jrsin ue Miqut Leluw urlade 30.u" (Enter Yjur unswen Jejceesul relecionihl dridFirid #% lre anule deviatundevibluninienlprisnanoleHINTWhite LixtllLhK Enaledeuialinrederl(6) #p"'dEvinticnblue IidhtNeed Help?Ct
The Jrsin ue Miqut Leluw urlade 30.u" (Enter Yjur unswen Jejcees ul relecion ihl drid Firid #% lre anule deviatun deviblun inienl prisn anole HINT White Lixtll LhK Enale deuialin rederl (6) #p"' dEvinticn blue Iidht Need Help? Ct...
5 answers
2.3.10Quostion HelpMonanbull? oul GIaimcianealtituda12 000- falls freely for 21 tnon opens nar puruchulu Jong tako her reach tne ground? AssuMe Iinear rosislunco vA/s taxing 716 witnoutina purachutu #no 1 6 MkIne parachuta. (Sugjgeslion: First determino hor helght above Ihu Oround and velocity when Ihe parachute opens;|It mal ake her seconds ench Ine ground (Round the nearest whole number neede D;
2.3.10 Quostion Help Monanbull? oul GI aimciane altituda 12 000- falls freely for 21 tnon opens nar puruchulu Jong tako her reach tne ground? AssuMe Iinear rosislunco vA/s taxing 716 witnoutina purachutu #no 1 6 MkIne parachuta. (Sugjgeslion: First determino hor helght above Ihu Oround and velocity ...
5 answers
Complete the table below by deciding whether precipitate forms when aqueous solutions and B are mixed If a precipitate will form; enter its empirical formula in the last column_Does precipitate form when and B are mixed?empirical formula of precipitatesolutionsolution Bbarium nitratepotassium chlorideyespotassium sulfideiron(II) chlorideyesiron(III) chloridesodium hydroxideyes
Complete the table below by deciding whether precipitate forms when aqueous solutions and B are mixed If a precipitate will form; enter its empirical formula in the last column_ Does precipitate form when and B are mixed? empirical formula of precipitate solution solution B barium nitrate potassium ...
5 answers
A function value and quadrant are given. Find the other five function values_ Give exact answerssin 0 =Quadrant IVcos 0-0 tan 0 = (Type an exact answer; using radicals as needed_ Rationalize all denominators )csc 0 = sec 0=L cot 0 =| (Type an exact answer; using radicals as needed_ Rationalize all denominators_
A function value and quadrant are given. Find the other five function values_ Give exact answers sin 0 = Quadrant IV cos 0-0 tan 0 = (Type an exact answer; using radicals as needed_ Rationalize all denominators ) csc 0 = sec 0=L cot 0 =| (Type an exact answer; using radicals as needed_ Rationalize a...
5 answers
1.5.8Desciibe all solutionsDaiancmnrot equivaent Ihe givon matrixx"Ll+xC (Tyne an integer Faction tor each matii:here
1.5.8 Desciibe all solutions Daiancmn rot equivaent Ihe givon matrix x"Ll+xC (Tyne an integer Faction tor each matii: here...
5 answers
X = (5 -2_ X
x = (5 -2_ X...
1 answers
Suppose a monatomic ideal gas is contained within a vertical cylinder that is fitted with a movable piston. The piston is frictionless and has a negligible mass. The area of the piston is $3.14 \times 10^{-2} \mathrm{m}^{2},$ and the pressure outside the cylinder is $1.01 \times 10^{5}$ Pa. Heat $(2093 \mathrm{J})$ is removed from the gas. Through what distance does the piston drop?
Suppose a monatomic ideal gas is contained within a vertical cylinder that is fitted with a movable piston. The piston is frictionless and has a negligible mass. The area of the piston is $3.14 \times 10^{-2} \mathrm{m}^{2},$ and the pressure outside the cylinder is $1.01 \times 10^{5}$ Pa. Heat $(2...
5 answers
Suppose Ais on mXn mctn Shel Hot He Kows A ce livocly_Inleee lod f av0 if Hu_Columns 5pan So Yoce }ly or€ #unqb +prove: ()If He_xows oe LI ten :_celumns Span1 ovl_(2) if H_Colunns spon_Hhaz xe fws of & LI
Suppose Ais on mXn mctn Shel Hot He Kows A ce livocly_Inleee lod f av0 if Hu_Columns 5pan So Yoce }ly or€ #unqb +prove: ()If He_xows oe LI ten :_celumns Span1 ovl_(2) if H_Colunns spon_Hhaz xe fws of & LI...
5 answers
Which of the following represent the strongest base?NaSHNaBrNaOtBuNaNH2NaOH
Which of the following represent the strongest base? NaSH NaBr NaOtBu NaNH2 NaOH...
1 answers
Simplify. $$\left(-3 b^{2}\right)\left(2 a b^{2}\right)^{3}$$
Simplify. $$\left(-3 b^{2}\right)\left(2 a b^{2}\right)^{3}$$...

-- 0.019660--