00:01
To determine the effect of 100 % nitrate on the growth of pea plant, several specimens were planted and then watered with 100 % nitrate every day.
00:08
At the end of two weeks, the plants were measured, and here is our data on seven of them.
00:15
Assume that these data are observations from a normal distribution.
00:20
The first thing they want us to do is they want us to find a 90 % confidence interval for mu.
00:31
So information from our data set, there are seven data values.
00:36
Sample mean is 15 .757.
00:39
The sample standard deviation is 1 .792.
00:45
So we're going to take that 15 .757 plus or minus 1 .645 times 1 .792 divided by the square root of 7.
00:58
We'll have 15 .757 plus or minus a margin of error of 1 .114 for an interval of 14 .643 to 16 .871.
01:14
For part b, now we're going to do a 95 % confidence interval for our standard deviation.
01:24
So we're going to need some kai squared values.
01:28
So we'll do kai squared of 0 .05 divided by 2, which would be 0 .025, with a degree of freedom.
01:35
Of six, and that has a value of 14 .4444.
01:41
I had to look that up in a table, so we have a kai squared table.
01:46
And then i do kai squared 1 minus 0 .025, which would be 0 .975, with a degree of freedom of six, because there were seven values in our sample, so that's 1 .2373.
02:03
So we're going to take six times our standard deviation squared...