Confidence Interval and Sample Size Calculation 1....

Confidence Interval and Sample Size Calculation 1. Hemoglobin levels in 11-year olds vary according to the Normal distribution with a standard deviation (?) of 1.2 g/dL. How large of a sample size is needed for the sample mean to fall within 0.5 g/dL of the population mean with a 99% confidence? 2. The Program Director of an undergraduate Health Sciences Program in a New England university is planning a tour for a group of students and their parents. The standard deviation (?) from the previous years’ tours is 40 minutes. How many tour records should he review to have 99% confidence that the sample mean is within 20 minutes of the population (?)? 3. The standard deviation (?) of 20-29 year olds body weight is 40lbs. How many adults will be needed to have 95% confidence? The sample mean weight is within 10lbs of the population mean weight. 4. The mean diastolic blood pressure of 100 individuals is 73 mmHg with a standard deviation (s) of 11.6 mmHg. Calculate the 99% confidence interval for the ?. 5. The mean weight of 100 men from the Honolulu Heart Study is 64 kg with a standard deviation (s) of 8.61 kg. Calculate the 99% confidence interval for the ?.

Transcript

00:01 So questions one, two, and three are all going to use the same formula, where we need to find the sample size based on the error and the confidence interval.

00:13 So the formula for that is the critical value based on the confidence interval, which i can get from this chart, times whatever the standard deviation is, divided by the error squared.

00:28 So in question number one, the information i'm given, is a standard deviation of 1 .2, the error is 0 .5, and i have a 99 % confidence interval.

00:42 So when i come down here to 99%, that will always give me a z value of 2 .58.

00:49 So now i simply need to substitute in the values, 2 .58 in place of z sub c, times the standard deviation divided by the error, squared.

01:11 So 2 .58 times a standard deviation divided by the error.

01:22 And that has to round up to the next whole number.

01:25 So 38 .3 becomes a sample size of 39.

01:32 Number two will be done the same way, except number two, our standard deviation, is 40.

01:42 Still the same confidence interval.

01:44 So it's a 99 % confidence intervals, so we're still going to use 2 .58.

01:49 But now we want the sample mean to be within 20 minutes, so that means the error is 20.

01:54 So my sample size will be 2 .58 times the standard deviation, divided by the error, all squared.

02:04 So 2 .58 times 40 divided by 20 squared.

02:13 And then i have to round up so that'll be 27.

02:17 So i would need a sample size of 27.

02:26 And then finally number three, standard deviation is 40.

02:32 The error, we want the mean to be within 10 pounds, but now my critical value is based on a 95 % confidence interval.

02:41 So i look at my chart and that's going to be 1 .96.

02:46 Everything else will be done the same way.

02:48 N will be 1 .96.

02:50 And will be 1 .96.

02:50 And will be 1 .9 times 40 divided by 10 squared.

03:13 So 61 .4656 would round to a sample size of 62.

03:25 Now, for the next two problems, i'm asked to find a confidence interval, but i do not know the standard deviation of the population.

03:37 Instead, for number four and number five, i'm given the sample standard deviation.

03:41 So i'm given s instead of mu.

03:47 So for 4 and number 5, i have to use a t table.

03:53 So my critical value is based on the degrees of freedom.

04:00 But the nice thing is it's still found the same way.

04:03 It's basically the mean plus or minus whatever the error is in my problem.

04:09 And the error is found by taking that critical value of t, which will find, from the table, multiplying it by the sample standard deviation and dividing it by the square root event.

04:27 Show in the case of number four, i want a confidence interval of 99 % .99.

04:34 I'm given a standard deviation of 11 .6, a sample size of 100, and a mean of 73.

04:43 So i come down here to my chart, and here is the 99 % confidence interval.

04:52 So i'm just going to look at this part of my chart...

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