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Point) There are three registers at the local grocery store. suspect the mean wait-times for the registers are different: The sample data is depicted below: The sec...

Question

Point) There are three registers at the local grocery store. suspect the mean wait-times for the registers are different: The sample data is depicted below: The second table displays results from an ANOVA test on this data with software claim there is difference in mean wait-times between the registers.Wait-times in Minutes Register 1.3 1.1 0.6 2.4 0.8 1.7 2.2 1.5 1.45 Register 2 1.8 2.3 2.1 1.9 1.7 1.9 2.1 1.975 Register 3 2.1 1,.7 1.4 2.1 1.7 1.5 1.8125ANOVA Results P-value 3.36767 0.0538828(a

point) There are three registers at the local grocery store. suspect the mean wait-times for the registers are different: The sample data is depicted below: The second table displays results from an ANOVA test on this data with software claim there is difference in mean wait-times between the registers. Wait-times in Minutes Register 1.3 1.1 0.6 2.4 0.8 1.7 2.2 1.5 1.45 Register 2 1.8 2.3 2.1 1.9 1.7 1.9 2.1 1.975 Register 3 2.1 1,.7 1.4 2.1 1.7 1.5 1.8125 ANOVA Results P-value 3.36767 0.0538828 (a) Test my claim at the 0.10 significance level. There is sufficient evidence to conclude that the population means are not equal: Yes No Does your conclusion change at the 0.05 significance level? Yes No



Answers

A grocery store chain has as one standard of service that the mean time customers wait in line to begin checking out not exceed 2 minutes. To verify the performance of a store the company measures the waiting time in 30 instances, obtaining mean time 2.17 minutes with standard deviation 0.46 minute. Use these data to test the null hypothesis that the mean waiting time is 2 minutes versus the alternative that it exceeds 2 minutes, at the $10 \%$ level of significance.

What's up? Sat cats in this video, we are given some raw data and we are asked to perform a one way Unova. And if the another test is significant, we are asked to them perform either a chef or a turkey test. So we are given this raw data and this is, ah, weekly er visits between different hospitals. So in order to perform an Innova, I'm gonna be using the data analysis package on Excel, which is also what the book uses. So we're gonna do a nova single factor, and our input range is gonna be all of our data. And we do have labels in the first row, so make sure that's checked. We are doing this at a 0.5 alfa levels to make sure that coincides with what kind of tests your doing. And then our output ranges just where it's gonna summarize those results for us. So says the results of our one way and over test and what we really want to look at is our critical value and our test statistic. So we will have a significant result if our test value is larger than our critical value. So is 3.76 larger than 3.68 Yes, it ISS, so we can reject our null hypothesis. So to summarize our results, we would say there is enough evidence to conclude that there is at least one mean that is different from another mean. So because we have a significant unova TAAS, we can go ahead and perform a post talk test. And if you look, um, our sample sizes are equal, so we're going to be doing a two key test. And the test statistic for this test is found by taking the mean differences and dividing that by the square root of our mean square within groups multiplied. Fine. I'm sorry. Did. And then we're gonna divide that by end, and then our critical value is found with the end tables. Let's go back to our Excel spreadsheets so we can do some calculations. So let's do Let's do our pairs first. So we're gonna pair ex and why? Why? And Z and the and X So let's take the mean difference. So we're gonna take mean difference of X and why, why? And see and Z and facts, and then we're going to take the square root of our means square with end groups to buy by our sample size, which is all six. All right. And then we can calculate our test statistic by taking our numerator divided by our denominator. Okay, so these are our test statistics. I noticed that one of them's negative, but, um, an F value is always gonna be positive. So we can just ignore that and just consider it a positive value. So to find the critical value, we are going to go to our and table. So Kay is the number of means we have, which is three. So we have three categories. We have hospital X, Y, and Z and V is our total population. So the sample size all of our sample sizes together. So six times three. And we're going to subtract K from that. So we're gonna take 18 minus three, so it's gonna be 15. So que is three and V is 15. So 3.67 is our critical value. All right, let's go to our white board so we can write this down. All right, so, in orderto figure out if we have a significant para not We're going to see if our test statistic is larger than our cook about you. So it was 1.77 larger than 3.67 No. Is 2.10? No. Is 3.87? Yes. So we have one significant pair. It's between hospitals, uh, X and Z. So there is sufficient evidence to claim, uh, a mean difference exists between hair three and one. All right, that's it for this video. You guys, I hope you learned a lot. And also in its time.

Theme. Each note is that the one is smaller than or equal to Muto, and each one in that New York is bigger than you. So the degree of freedom, which is in one lost in two miles to I mean, which is equal to fit. So the critical, very correspondent is toe degree freedom, equal to 50 and off, April toe open or five one tail. So using Table five is equal to 1.6 seventies. So the fool the standard deviation, which is equal to square root off and one minus 1 20 to minus one times this one square 0.89 square well in the Tu minus one. So 13 minus one times is to square as 2.7 mine squared over and 1% from minus, which is 22 plus 30 minus two, which is ableto open a 30. So the distance statistic so T is equal to x one bar one x two so fine by forcing one that's 5.12 Oh, which is open 833 square root off one over and one yes, one over and to which is equal to 1.454 So if the value of this this is is in the rejection reasons and now have process rejected, So as 1.454 is smaller than 1.676 Okay, so we fail to reject the null hypothesis you

All right, so in this problem we are running a hypothesis test against um what the uh no hypothesis of our mean household income Is 4,048,750. And we are running a test that it is different Then 48,750. And we're gonna test it at the 10% significance level based off of our sample that is given. So what we're gonna do here is we're going to calculate our test statistic which is our Z score, our Sample was 51,505. And we're going to subtract are null mean divided by our standard deviation divided by the square root of our sample size. And when we work out that formula for the Test statistic, that gives us a Z. score of 2.54. Now this is a two tailed detest. Um because it is we're looking at if it's just different than what we had before. So then what we're gonna do is we're going to take our significance level and divide it by two. And looking at our chart, we get the value 1.645 is where our rejection region is gonna lie. So anything outside of Um negative 1.645 and positive 1.645 would be remains to reject the null. And we're gonna be right in here with our 2.54. So with this one we are going to reject the null hypothesis now um that was part a part B. We're going to be doing a very similar thing, but we are going to do it at um we're just going to do the alternate hypothesis that the mean is greater than 4807 50. So now our rejection region is just gonna be on one side. So this area, the 10% rejection region is only on the right hand side now. So we have to use we don't split our significance level in half for our Z. Score. And when we do that we get a Z score of 1-8. Clearly still going to be even more so in the tail now in the rejection region. So here in part B, we would also reject an all because our Z score falls in the rejection region.

So the variable under consideration is hours slept. The two populations we are looking at is some a long word. Virtual. Just abbreviate to LH And the second one there is one C. Is going to be just be the differences between these populations. Okay. And can we use these differences? Yes we can. Since they are differences. Yeah. So our alternative hypothesis is going to be the thing that one of them is greater than the other. Actually it's gonna be, the first one is greater than the other. So um you want greater than youtube making that a right tailed test. Now they give us that D. bar is 2.33. So put that there & SD. is 2.02. Mhm. Yeah. And we have how many samples? 345 10. So two divided by Square root of 10. This is going to be approximately equal to let me bust out my calculator here. 2.02 Divided by Square Root of 10. 2.33 divided by 6.66 there. Yeah .63. This is about equal to 3.680. This is going to get us a p value of Oh, I gotta go all the way back the book here. It wasn't at the right page. And by analysis of critical values 3.688 lands as well, past the 1.833 for the 5% critical value And for the 2.4-1 critical value at the 1% significance level. So in both cases, we will reject the null hypothesis.


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