### 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 xdifference = 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 µdifference = 0. For this test the hypothesis of no change, the null hypothesis, is:
H0: µdifference = 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: µdifference ≠ 0

Run the hypothesis test at an alpha of α = 0.05

1. _________ How many degrees of freedom are there?
2. _________ Determine tc
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 xdifference = 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 µdifference = 0. For this test the hypothesis of no change, the null hypothesis, is:
H0: µdifference = 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: µdifference ≠ 0

Run the hypothesis test at an alpha of α = 0.05

1. _________ How many degrees of freedom are there?
2. _________ Determine tc
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 learn the material between Monday and Wednesday?
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?
8. __________________ Where was Duke Paoa Kahanamoku born?
9. __________________ In what sport did Duke Kahanamoku win a gold medal in the 1912 Olympics?
10. __________________ 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