00:01
Okay, and your question, you're given the information that a simple random sample of 90 items resulted in a sample mean of 70, the population standard deviation is 10, and part a you're supposed to compute a 95 % confidence interval for the population mean.
00:17
So the first sample or the first question, part a, is dealing with that 90 sample size.
00:25
And for a 95 % confidence interval, for this question, basically we're going to take our sample.
00:30
Mean 70 then it's going to be plus or minus what we call z star or a critical value this is one you would want to memorize a critical value for a 95 % confidence interval is 1 .96 so that's one that you should memorize because 95 % confidence intervals are very common if you needed to find it this is where your question is saying reference a z table z star is is the value on the upper half of the 95 % that's in the middle.
01:07
So you would look at your chart and say there's 2 .5 % down here, 2 .5 up here.
01:14
You would look at a z table and combine these two values to 0 .975.
01:21
And you'd look for the z value that represents this area.
01:26
Okay, but it's better to have that one memorized because it's a more common one that we use.
01:34
So for part a to finish up our confidence interval, i'm going to find the next part of the formula, which is called the standard error.
01:42
And to do that, i take the standard deviation 10, and i'm going to divide it by square root of the sample size.
01:49
And that works out to be, for your question, 1 .0, we're only going two decimal places, so 05.
02:01
So for part a, you would have 70 plus or minus 1 .96 times 1 .05.
02:11
Now, i am going to multiply by the more accurate version of 1 .05 when i do this.
02:17
And it'll be 70 plus or minus 2 .07 is rounded to two decimal places.
02:29
So the low amount, which you're supposed to provide, the low amount would be 70 minus 2 .0...