Hypothesis testing

[catpurr57]

I get a means score of 25. what do I do after that?

Evolutionary theories often emphasize that humans have adapted to their physical
environment. One such theory hypothesizes that people should spontaneously
follow a 24-hour cycle of sleeping and waking—even if they are not exposed to
the usual pattern of sunlight. To test this notion, eight paid volunteers were
placed (individually) in a room in which there was no light from the outside and
no clocks or other indications of time. They could turn the lights on and off as
they wished. After a month in the room, each individual tended to develop a
steady cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23,
24, 25, 26, and 25.
Using the .05 level of significance, what should we conclude about the
theory that 24 hours is the natural cycle? (That is, does the average cycle length
under these conditions differ significantly from 24 hours?) (a) Use the steps of
hypothesis testing. (b) Sketch the distributions involved.

 

[tkhunny]

That is some excellent typing. What is your plan for solving the problem and doing the required work.

 

[catpurr57]

After obtaining the means score, the median, and the range, I am unsure how to get the variance and standard deviation.
If the means = 25
median = 25
range = 4

I read and reread the descriptions in the book, but it just does not compute in my brain.
I am the type of person that needs someone to spell it out for me step by step when it comes to this class and I have been unable to find anyone that can do that with me.

 

[galactus]

\(\displaystyle H_{0}: \;\ {\mu}=24\)

\(\displaystyle H_{a}: \;\ {\mu}\neq 24\)

The SD can be easily found by running the data through most any calculator. Excel as well.

The Critical Value is found by looking up the t score for 7 d.f, two-tails, and alpha=.05 in the t table.

A t distribution is used because the sample size is only 8.

The test stat can be found by using \(\displaystyle t=\frac{(x-{\mu})\sqrt{n}}{s}\)

Check the test stat against the CV. If the test stat is larger than the CV, inside the rejection region, then reject H0.

 

[catpurr57]

okay, I got a variance of 1.25 and a SD of 1.118. Is this correct?

 

[galactus]

No, not quite. The SD is \(\displaystyle \frac{\sqrt{70}}{7}\approx 1.195\)

 

[catpurr57]

okay, I forgot to take the N-1, so the d.f. is 7, then divide 10 by 7 getting 1.429 squared is 1.195. I see that part now.
In order to do this problem, do I need the Z score? If I am doing this right the z score would be -0.84?

 

[catpurr57]

How do I sketch the normal curve with all this information?

 

[galactus]

No, as I said in my original post, this is a t distribution. You use a t when \(\displaystyle n\leq 30\).

Do you have a t table?. It is NOT -.84

 

[catpurr57]

the t table shows 2.36 with a d.f. of 7

 

[galactus]

Yep, that's the one.

Now, check that against your test stat: \(\displaystyle \frac{(25-24)\sqrt{8}}{1.195}=2.36688\)

The critical value you just found is 2.365

The test stat is just a hair larger than the critical value. That means a rejection of the H0.

What does that mean?.

 

[catpurr57]

the hypothesis is rejected because the critical value is smaller. the cut-off score is 2.36. How do I show this on a normal curve diagram?

 

[galactus]

Just draw the normal curve and label it with your information.

Also, when I ask about 'reject H0', I meant the interpretation. What does this mean in relation to the 24 hour cycle?.