00:01
Our question says that a researcher is going to estimate the average typing speed of students of a college.
00:05
He select a random sample of 20 students and finds the average typing speeds to be 70 words per minute.
00:11
And the standard division is 5 words per minute.
00:13
So estimates the lower bound of the 80 % confidence interval of the average typing speed of the students of this college.
00:21
So let's extract out the sample details.
00:23
We have our n is equal to 20.
00:25
We have our sample in x bar to be equal to 70 words per minute and we have our sample standard division to be equals to five words per minute our confidence level is 80 percent we're supposed to construct a 80 percent confidence interval so to do so we have the format that says m is equal to x bar plus or minus the critical value times s divided by the square root of n so we have all of our details ready aside from the critical value now our critical value is going to be based on either a t score or is this called.
01:00
Now we have a very small sample size, a sample size of 20, which simply implies that our critical value is going to be a t score because according to the central limit theorem, when the sample size of a sample distribution is greater than or equals to 30, it's going to be defined by a normal distribution.
01:17
Otherwise we use a t distribution.
01:19
So if our confidence levels 80%, our alpha level is going to be 20%.
01:24
So let's try to get the critical value...