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Question 132 ptsSuppose that you have a sample of size n-14 with mean 7 and sample standard deviation s-4_A 95% confidence interval for the population mean; LJ, is ...

Question

Question 132 ptsSuppose that you have a sample of size n-14 with mean 7 and sample standard deviation s-4_A 95% confidence interval for the population mean; LJ, is closest to:(4.591,6.409)(4.780, 6.146)(4.691 ,9.310)(4.780,9.220)

Question 13 2 pts Suppose that you have a sample of size n-14 with mean 7 and sample standard deviation s-4_ A 95% confidence interval for the population mean; LJ, is closest to: (4.591,6.409) (4.780, 6.146) (4.691 ,9.310) (4.780,9.220)



Answers

Assume the sample is from a normally distributed population and construct the indicated confidence intervals for $(a)$ the population variance $\sigma^{2}$ and $(b)$ the population standard deviation $\sigma .$ Interpret the results. The diameters (in inches) of 17 randomly selected bolts produced by a machine are listed. Use a $95 \%$ level of confidence. $$\begin{array}{llllll}4.477 & 4.425 & 4.034 & 4.317 & 4.003 & 3.760 \\3.818 & 3.749 & 4.240 & 3.941 & 4.131 & 4.545 \\3.958 & 3.741 & 3.859 & 3.816 & 4.448 &\end{array}$$

All right, So we're given this set of eight points that comes from our sorry eight data points that come from a norm population. And we have some questions. Ask. So first off, what's your point estimate for the population mean or a point estimate for the population mean sorry. Equal sign is not technically after it. It's gonna be whatever sample mean is, uh, when you have these up, this becomes 10. 18 30 45. 50. There should be an 11 in here. My bad. So 10 18 30 45. 50 uh, 56 67 80. Yep. That was just a sandy check for me. Just making sure I had all the plot point that anyway, So All right. What's your point? Estimates. Come on. There we go. For standard deviation. Well, that's just gonna be the standard deviation of the sample, which, if you do the mathematics for which I'm not going to do by hand right in front of you, you're gonna get three points. 464 All right, now to find hour interval at and 95% confidence. So we want to find out margin of error in party and because we do not have a given population standard deviation. We only have ah, point estimate. Oops. We're going to use a tea interval. So it's gonna be tea time. Standard deviation over skirt and equals eight. We look a t star, we have n equals AIDS. So our degrees of freedom, which is an minus one, is gonna be seven. We check our tea table at seven degrees of freedom for 95% confidence. We get, uh, 2.365 All right, so this equals 2.365 times 3.464 divided by the square root of eight. Punch that in on our calculator and we get So this is about 2.8964 All right, finally, we're gonna constructor confidence Interval. All right, so Oops. There we go. So 10. Plus, he's simple. It's just 12.8 964 and subtracting out. You'll get some 0.1036 There's your interval. My pen's acting weird. Come on. There we go. And there you have it

Okay. So in this case we want to test the claim that the population mean is equal to 40. Great. Okay, so what is going to be the null hypothesis? My main is 40. So my nail hypothesis is that this is equal to 40. My null hypothesis that Mueller's 40 and my alternative hypothesis will be that new is not equal to 40. Okay, now, uh the status and all visited the alternative hypothesis as well. We do not have any information regarding how the population mean might differ from 40. Okay, so which means that this null hypothesis is this alternative hypothesis is correct? We do not know if means less than 40 or greater than 40. So, well, right, this is not equal to so this is our part a this is our part fee. Let us move on to part C. Part C says state the alternate hypothesis. If you believe based on the experience of pasta is that the population mean may exceed 40. So in that case the alternative hypothesis will be Mu is greater than 40, right, moving on to part deep. Stay. The alternate hypothesis, if you believe based on past experience of our study, is that the population means maybe less than 40. So in this case, what is the alternative hypothesis? Me less than 40, Right, So these are my answers, Yeah.

Mhm. So in this problem we are finding the 99 confidence interval for a mean of 55, A simple size of 16, A standard deviation of five And our confidence level of 99%, so confidence level of 99 has a Z score That is equal to 2.58. We're gonna plug it into our formula, so X bar plus or minus my Z score times, my times my standard deviation divided by the spirit of my sample size, So that is 55 plus or -2.58 Times five, divided by the skirt of 16. And this gives me a lower bound of 51.78 and an upper bound of 58.23. So we have a 99 confidence interval, that is between 51.78 and 58.23.

And this problem we're given three different scenarios and we want to know when can we use this E interval, a procedure to find a confidence in the world for these um different different situations. So the first one for a It says that our sample size is 10. Mhm. So on this one we're not going to use we're not going to use the z integral. Right? Because the sample size is less than 30 and that's our standard right there. So if our sample size is Um equal to or greater than 30 then we can use the c. interval. If it's not greater than 30 then we're not going to use this interval. So let's look at our other choices to be has a sample size of 72 sorry, 75. So on this one, yes we could use the the interval because the sample size Is greater than 30. And then for our last one answer choice C has your choice but section see our sample sides is 20. So in this case we're not going to use the sea interval mm because the sample size is less than 30


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