Quiz 09 | 10 • Name:

A sample size n = 43 students had their body fat measured in January and again in May. There was a sample mean x_difference = 0.44 change in the paired differences with a standard deviation of sx = 1.40
Run a hypothesis test that this data could not include a population mean µ_difference = 0. For this test the hypothesis of no change, the null hypothesis, is:
H₀: µ_difference = 0.

The alternate hypothesis is that a change has occurred, that a the data taken could not include the possibility of a change of zero, is:
H₁: µ_difference ≠ 0

Run the hypothesis test at an alpha of α = 0.05

1. _________ How many degrees of freedom are there?
2. _________ Determine t_c
3. _________ Find the t-statistic t. Use µ = 0.
4. Do we:
   1. ___ Reject the null hypothesis? OR
   2. ___ Fail to reject the null hypothesis?
      
      
5. ___________________________ Did the students in the course gain body fat between January and May?
6. _________ What is the p-value for this hypothesis test?
7. _________ What is the largest possible confidence interval, max c, for which this difference is significant?

A sample size n = 38 students took the Duke Kahanamoku pre-test and post-test. There was a sample mean x_difference = 0.89 change in the paired differences with a standard deviation of sx = 1.16
Run a hypothesis test that this data could not include a population mean µ_difference = 0. For this test the hypothesis of no change, the null hypothesis, is:
H₀: µ_difference = 0.

The alternate hypothesis is that a change has occurred, that a the data taken could not include the possibility of a change of zero, is:
H₁: µ_difference ≠ 0

Run the hypothesis test at an alpha of α = 0.05

8. _________ How many degrees of freedom are there?
9. _________ Determine t_c
10. _________ Find the t-statistic t. Use µ = 0.
11. Do we:
    1. ___ Reject the null hypothesis? OR
    2. ___ Fail to reject the null hypothesis?
       
       
12. ___________________________ Did the students learn the material between Monday and Wednesday?
13. _________ What is the p-value for this hypothesis test?
14. _________ What is the largest possible confidence interval, max c, for which this difference is significant?
15. __________________ Where was Duke Paoa Kahanamoku born?
16. __________________ In what sport did Duke Kahanamoku win a gold medal in the 1912 Olympics?
17. __________________ What lost sport did Duke Kahanamoku revive?

Statistic or Parameter	Symbol	Equations	Excel
Hypothesis Testing
Degrees of freedom	df	= n-1	=COUNT(data)-1
Calculate t-critical for a two-tailed test	tc		=TINV(α,df)
Calculate a t-statistic (t)	t		(x - µ)/(sx/sqrt(n))
Calculate a p-value from a t-statistic t	p		= TDIST(ABS(t),df,#tails)
Calculate a maximum possible level of confidence c from a p-value (two-tailed)		max c = 1-p