In a sludy of Ihe accuracy of fast food drive-through orders, Restaurant A had 276 accura orders and 67 that were not accurate. Construct a 95% confidence interval ...

Use the data and confidence level to construct a confidence interval estimate of $p,$ then address the given question. In a study of the accuracy of fast food drive-through orders, Burger King had 264 accurate orders and 54 that were not accurate (based on data from $Q S R$ magarine). a. Construct a $99 \%$ confidence interval estimate of the percentage of orders that are not accurate. b. Compare the result from part (a) to this $99 \%$ confidence interval for the percentage of orders that are not accurate at Wendy's: $6.2 \%<p<15.9 \% .$ What do you conclude?

Okay, so over here we are given a sample off 362 orders off which 33 were not accurate. So in the first one, we want to find the best point estimate for the population proportion. And it is nothing but p cap the sample proportion, which is given by this 33 by 3. 62 which is 0.911 Next, we want to identify the margin of error, so this actually will become R P. Cap. This will be our P cap. So what will be Q Cap que cap will be one minus speaker when minus speak camp. Okay, now we want in 95% confidence interval, which means our Alfa by two is 0.25 and Z Alfa by two becomes 1.96 So what is the formula for margin off error? The formula for margin off error is this term multiplied by the value the value that we found for the Alfa by two. And this actually gives me 0.297 All right, now let's move to Park si in party, we want to construct a confidence interval. So I have the proportion. I have the sample proportion Peak cap. I also have e How do I construct the confidence interval? It is going to be p cap plus minus C and this is the interval that I get B is from 0.615 to 0.1 to 1. This is my proportion. And how will I interpret this? I will say that I'm 95% confident that the true proportion off the orders that were not accurate lies between 0.615 and 0.1 to 1. These would be my answers.

Okay, This question says Refer to data set 25 fast food and constructed 95% Confidence interval estimate off the main drive thru service Time for McDonald's at dinner and then do the same forward looking at dinner and then compared the results. First we're going with McDonald's, this data said. You will get online. The link is actually given in the text book. You can go to that link and get your hands on this data set. The first one is the analysis of McDonald's and is 50 comprehensive double 0.95 First we're calculating the mean and then the standard deviation. The degree of freedom is in minus one that is 49 handle. Uh, since our confidence interval is 95% we're going toe get Alfa by two is equal to 0.25 Using this Alfa and this degree of freedom of 49 we get critical devalue as 2.14 and we substitute these values in the formula for margin of error, which turns off with 17.9263 on the confidence interval becomes 1 61.391 61.39 1. 97 0.24 This is my confidence in trouble. Yeah, the next we move on to Burger King and over here also we C n s 50 confidence level is 95%. This is the mean. This is the standard deviation we are taking in minus one in the denominator because it's the sample standard deviation Degree of freedom is 49 and P Alfa by you will remain the same, which is 2.41 as degree of freedom. The same on the confidence level is also seen again. We calculate the margin of error and this time our present double dunce out to be 1 39 1 39 1 39.11 to 1. 67.48 Okay, how do these two compared to each other? One is from 1. 61 to 1 97 and one is from 191 67. So we cannot say that these two are much different because they are overlapping. There is an overlap between their confidence intervals at 95% confidence. So we do not have enough evidence to say that these two have different means. These two are different mean times

So in 1 15 we're looking to see if there's an interval for the situation they gave you. So on this one, you Since you really don't need to show work, you can get all your information from the calculator. So if you go to stat over the test, you want to go to the tea interval on my calculator, It's number eight. So if you just put in the information for explore SX and and then the confidence level that will give you is letter B.

Into this lesson and this lesson we have this data to solve questions. Now we are looking at the best estimate for the population proportion trip. So the best estimate would be Yeah the number that Is for yes. All over the total number. And that is 5:31. All over 1002. So In three small places water We have Joe on five two. Yeah Let's take for the small places they work on 5- 99. All right. That is the first pad the second part. We are looking at the maiden of error. E. So the margin of L. E. C. Call to the critical value. Mhm. Times the P. Do you have calculated then? Schools of that -1. The sample proportion all over the total number. So when this let's look for the critical value. So we have The offer which is equal to 0.05. So this will become 04 and zero 25. Yes. Yeah. So we are looking at about 1997.5 President of the area to the left. And let's find that from the table. So 97.5 97.5%. And that is here. So 1.9 last 0.06. And that is 19. 1.96. Yeah. So with that we have on 96 times The P which you found us 0.5299 0.5299 one. Mine is their .5299. All over one. There was there were two. Yeah. So with that we have and I post made value of the margin of error. Yeah. Oh 0.0 Thursday Night that's the margin of error. The not as bad as to what write a statement that correctly interprets the confidence interval. The CPA do look at the confidence interval. Uh huh. So confidence interval, the proportion. Mm hmm mm. Yeah. Now we have the interval like this. Mhm. Yeah. You So that is 0.8-9 9 -0.0309. Mhm. Then we have a positive assemble that. Yeah. Mhm. Yeah. Mhm. So 0.8-9 nine Uh 5 to other. You have a 52. Yeah. Then if we subtract their zero 309 from it, that is 30.4 99. And here we have zero falling 56 08. Yes, so this is the confidence interval of the proportion the last part C Yeah, so we are interpreting this we uh 98% Uh was 95. So we are 95 questions confident that's the proportion. Okay, it's between yeah. Oh 0.499, Cool. And their .5608. All right, so this is the data a operation thing. Thanks for the time. This is the end of the lesson