A random sample of 25 observations was selected from a...

A random sample of 25 observations was selected from a normally distributed population. The average in the sample was 84.6 with a variance of 400. a). Construct a 90% confidence interval for μ. b). Construct a 99% confidence interval for μ. c). Discuss why the 90% and 99% confidence intervals are different. d). What would you expect to happen to the confidence interval in part (a) if the sample size was increased? Explain your answer.

Transcript

00:01 So in this question sample mean is given as, sample mean is given as 84 .6.

00:06 And sample standard deviation s is given as 20, small s.

00:12 Sample variation is going to be 400 and any sample size is given as 25.

00:18 So standard error of mean is going to be standard error of mean is going to be small s divided with under root end.

00:29 So this is going to be 4 approximately 4 value because we are dividing 20 divided with under root and 25.

00:36 So this is like under root 25.

00:39 So this is going to be 4.

00:40 So a point estimate of population mean mu is x bar equals to 84 .6.

00:49 So the critical point, critical value of t is going to be.

00:57 So the critical value of t is the critical value of t is the critical.

01:04 Value of t is going to be 1 .71 at this rate so this is going to be at 90 % interval the margin of error is going to be at 90 % confidence confidence confidence confidence interval the margin of error is going to be equal to s to as you added with under root n multiplied with t multiplied with critical value of t so this is going to be multiplied with t critical so this is going to be 20 divided with under root 25 multiplied with 1 .7 1 so this is going to be a standard error margin of error is going to be 6.

02:11 Approximately after calculation 6 .840 so a 90 % confident interval um of population mean is going to be at 90 % confidence interval the population mean is going to be the population mean mu is going to be x bar plus minus as under root n and the critical value of t which is going to be tc so we know that x bar is given as 74 .6 plus minus we have calculated it as 6 .840...

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