It is believed that college math students average less than...

It is believed that college math students average less than seven hours of sleep per night. A survey of 20 General Education Statistics students generated a sample mean of 7.54 hours with a sample standard deviation of 1.63 hours. Unfortunately, the population standard deviation is unknown. Let the level of significance be equal to 5%. What is the distribution to be used in this hypothesis test? Let x be the distribution of hours of sleep per night. Choose the correct option: a)x∼t_(19) b)x∼N(7.54,1.63) c)x∼t_(20) d)x∼N(7.54,(1.63)/(sqrt(20)))

Transcript

00:01 We know that the amount of sleep college students got at this particular college has a mean mu of 6 .7 hours with a standard deviation sigma of 1 .5 hours.

00:11 We aren't looking at individuals, we're looking at a sample of size 40.

00:15 We want the probability their sample mean x -bar will be less than 7 .1.

00:21 Okay, so i don't know the shape of the original distribution, but i do know that if i were to take every possible sample of size 40, take the sample means and plot them out, i would get something approximately normal because of the central limit theorem, which states that as sample size increases, sample means become more and more normally distributed.

00:42 If n is 30, approximately normally distributed, even if you don't know the shape of the distribution of the population.

00:49 It also tells me that the mean of the means is the same as the population mean and the standard deviation of the sample means, the standard error, is sigma over root n, so 1 .5 over root 40.

01:02 So we have a normal distribution question.

01:05 7 .1 is above the mean, we want less than, so area to the left.

01:11 To find this, you need something with the normal distribution already built in.

01:15 You could use a...

01:18 Okay, it says to round your standard deviation to two decimal places.

01:21 The answers are at two decimal places, so don't worry about it, basically.

01:26 The accuracy it's asking for here is so low, but we don't really have to worry.

01:30 You can also use a z -score table, which usually i wouldn't do unless told to, because it makes you lose accuracy...

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