00:01
For this problem to begin, in part a, we have that our null hypothesis would be the claim that the population standard deviation is equal to 10 beats per minute.
00:11
Since that is not a directional claim, our alternate hypothesis, or it's written as h1 in the notation there, our alternate hypothesis would just be that sigma does not equal 10 beats per minute.
00:23
So we would want to choose option d as listed.
00:26
For part b, calculating our test statistic, our chi -squared statistic here, is going to be equal to our sample size minus 1 times our sample variance divided by our population, or our hypothesized population variance.
00:43
So plugging in our given information, we know that we took a sample of size 30, so n -1 would be 29.
00:49
We have a sample standard deviation of 7 .1 beats per minute squared, or pardon me, the standard deviation was 7 .1, so the variance would be 7 .1 squared.
01:01
Then we have a null hypothesized variance of 10 squared.
01:05
So calculating that out, we have that our test statistic is going to be 14 .619, roughly.
01:13
Now for part c, to find the p -value, what we'll do quickly here is i'll note that we would have n -1 degrees of freedom, so we would have 29 degrees of freedom.
01:26
And i'll check if i actually have that chi -squared value on my table here, or something close.
01:33
So we have, for 29 degrees of freedom, i have a bunch of other tables around here, but trust me, this one's a chi -squared distribution table...