Confidence Intervals and Introduction to Hypothesis...

Confidence Intervals and Introduction to Hypothesis Testing 1) Calculate a 95% and 99% confidence interval for the following data set. Note: this is a sample. Show your steps including the mean, z-score, standard deviation, and standard error that you use. 12 10 18 16 11 10 9 17 6 13 10 20 21 24 18 17 19 12 11 10 2) In an experimental treatment, a random individual scores 51 on a measurement. People in general are normally distributed with a mean of 37 and a standard deviation of 7. The researcher predicts that the treatment will create an effect on the subject, but does not specify if the measurement will increase or decrease. Using a 5% significance level (p < .05), what conclusions should this researcher make about the treatment. Utilize the five-step hypothesis testing process and show all of your work.

Transcript

00:01 On question one, we want to find both a 95 % confidence interval and a 99 % confidence interval for the mean.

00:09 And i entered my data into my calculator, and we are going to be calculating a t interval.

00:19 And that's because we don't know the population standard deviation.

00:23 And so the statistics that i got for this, and let me quick just get those statistics.

00:30 For you.

00:34 The first statistic is the mean and the mean of those values comes out to be 14 .2.

00:40 The sample standard deviation is 4 .8 -297 and our sample size is 20.

00:49 And so our 95 % confidence interval will be to take 14 .2 plus or minus.

00:57 And then the t value that has 0 .25 in the upper tail and has has 19 degrees of freedom is 2 .03.

01:07 And our standard air is right here.

01:10 That's that 4 .8297 divided by the square root of 20.

01:15 So that's our standard air.

01:18 And there's our standard deviation right there.

01:22 And our appropriate t value and so on.

01:24 And when we do that calculation, we find out that that interval is 11 .94 to 16.

01:34 Point four six.

01:35 Now we're going to calculate a 99 % confidence interval and we know that that interval is going to get wider because now we have to use the t value with 0 .005 in the upper tail and 19 degrees of freedom and everything else stays the same and this is two point let me quick read i can't quite read my writing here 2 .861 and then we use the same standard error that 4 .8297 divided by the score root of 20 and that interval comes out to be and let me quick give you that the low limit of this and remember it's going to be wider because we're more confident is 11 .11 and 17 .29 now on the next question question two we're looking at a sample was taken of one and we get 51 as the value and we know this comes from a normal population that has a mean of 37 and a standard deviation of 5.

02:48 And we would assume that the distribution is going to be 30, have a mean at 37...

Question

Please give Ace some feedback