Save mesis Tests for a K Question 7, 10.3.19 Part 1 of 3 HW...

Save mesis Tests for a K Question 7, 10.3.19 Part 1 of 3 HW Score: 8.11%, 3 of 37 points O Points: 0 of 7 One year, the mean age of an inmate on death row was 40.1 years. A sociologist wondered whether the mean age of a death-row inmate has changed since then. She randomly selects 32 death-row inmates and finds that their mean age is 39.4, with a standard deviation of 8.3. Construct a 95% confidence interval about the mean age. What does the interval imply? Click the icon to view the table of critical t-values. Choose the correct hypotheses. Ho: H1: (Type integers or decimals. Do not round.) ve this View an example Get more help - Q 80 MacBook Air ? DII DD 4 F9 F10 Clear all Check answer 4 + F12

Transcript

00:01 Hello, welcome to this lesson in this lesson.

00:03 We're giving the mean age of human image on death row a year ago that was 38 .4 years and sociologists wonder whether the mean age of the death row image have changed since then so she randomly selects 30 32 death row image right so the sample size is 32 and find that the mean age is 36 .6 so here the sample mean is equals to 36 .6 alright, so we would look at the 95 % confidence interval and explain what it means right? whether this interval still contains the mean age that was a year ago, which is 38 .4 so the part one of this question you will choose the correct hypothesis here we have the null hypothesis which says that the population mean is equals to 38 .4 right and the alternative hypothesis it says that the population mean is not equals to 38 .4 so that's for part one the part two you would construct 95 % confidence interval for the true population mean of the mean age the image of the image so here we use three steps to do this let's have step one which is identifying the point estimate the point estimate is the single point below which we have the lower bound above which we have the upper bound so here the point estimate is the mean the sample mean which was giving us 36 .6 alright, then let's look at the step two where we find the margin of error the margin of error is what we subtract from the point estimate to get the lower bound and we add to the point estimate to get the upper bound of this 95 % confidence interval this is calculated as the z -score for 90 % confidence interval times the standard deviation divided by the square root of the sample size so given that the population is the population size is 30 the sample size is 32 we will use the z distribution to do this so here the z for the z value for 95 % confidence interval is equals to 1 .96 here we have the margin of error which is going to be 1 .96 times the standard deviation which is 8 .4 divided by the square root of 32 alright, so here we have e which is equals to 16 .464 divided by square root of 32 now let's have it to two decimal places here we have 4 .06 that is the margin of error let's step three we proceed to find a 95 % confidence interval so here we have the sample mean plus or minus the margin of error so for the lower confidence bound we'll have the mean minus the error and the mean plus the error as the upper bound.

04:43 So we talking of 36 .6 minus 4 .06 36 .6 plus 4 .06.

04:57 So here we have the mean population age which is between 32 .54 for the lower bound upper bound 40 .66...

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