Texts body temperature is known to be distributed normally...

Texts: Body temperature is known to be distributed normally among healthy adults. You collect data from a random sample of 20 healthy adults and find that your sample temperatures have a mean of 98.4 and a sample standard deviation of 0.3 (both in degrees Fahrenheit). What is the 95% confidence interval critical value you will use? Group of answer choices: 2.086 1.961 1.645 2.093 A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent Rockford newspaper. The following data were collected: 20¢; 75¢; 50¢; 75¢; 30¢; 55¢; 10¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal. Construct a 95% confidence interval for the population mean worth of coupons. Find the lower limit of the confidence interval. Enter it rounded to the nearest cent (2 decimal places). Group of answer choices: $0.33 $0.36 $0.44 $0.35

Transcript

00:01 Once again, welcome to a new problem.

00:05 This time we're dealing with inferential statistics.

00:08 We're dealing with inferential statistics.

00:11 And when it comes to inferential statistics, we have two branches.

00:16 We have confidence intervals.

00:21 We have confidence interval and we also have hypothesis testing.

00:27 So we have confidence interval on one hand and we have hypothesis testing.

00:32 On the other hand, we could have confidence interval for means and we can also have confidence intervals for proportions.

00:48 We have confidence intervals for means and confidence intervals for proportion.

00:56 And so if we deal with confidence interval for means and we have sample data, then for the most part we have x bar plus minus margin of error where the margin of error is t alpha over two based off of the degrees of freedom n minus 1 and s of radical n remember s is the standard deviation s is the standard deviation and n is the sample size.

01:31 So s is the standard deviation and n is the sample size.

01:36 So coming back to this problem, we have temperatures.

01:42 We have temperatures in fahrenheit.

01:52 And this is in the month of june.

01:54 That's like summertime.

01:57 And the sample is 17.

02:00 Us cities and so the numbers we have for the sample is for the temperatures is 78 105 91 80 101 93 so these are numbers that you're gonna input into your calculator 92 78 we're going to that 70, 91.

02:37 Remember we have 17 of them.

02:40 We have 101, 71, 81, we have 84, we have 1 -2, 70, and 86.

02:52 So these are numbers that you're plugging in.

02:55 And so the temperatures, the temperatures have a normal distribution.

03:06 The temperatures have a normal distribution, meaning that they're going to be bell shaped.

03:14 And we want to determine a 92 % confidence interval.

03:24 So we want to figure out what the 92 % confidence interval.

03:29 For me, which stands for the population mean, so we want to see the confidence interval for that.

03:40 We also want to determine the distribution used.

03:45 We want to determine the distribution used.

03:49 We also want to determine the mean and the standard deviation.

03:54 So these are values that we're looking at, you know, the mean, the distribution use, the standard deviations.