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:

H_{0}: 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:

H_{1}: µ_{difference} ≠ 0

Run the hypothesis test at an alpha of α = 0.05

- _________ How many degrees of freedom are there?
- _________ Determine t
_{c} - _________ Find the t-statistic t. Use µ = 0.
- Do we:
- ___ Reject the null hypothesis? OR
- ___ Fail to reject the null hypothesis?

- ___________________________ Did the students in the course gain body fat between January and May?
- _________ What is the p-value for this hypothesis test?
- _________ 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:

H_{0}: 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:

H_{1}: µ_{difference} ≠ 0

Run the hypothesis test at an alpha of α = 0.05

- _________ How many degrees of freedom are there?
- _________ Determine t
_{c} - _________ Find the t-statistic t. Use µ = 0.
- Do we:
- ___ Reject the null hypothesis? OR
- ___ Fail to reject the null hypothesis?

- ___________________________ Did the students learn the material between Monday and Wednesday?
- _________ What is the p-value for this hypothesis test?
- _________ What is the largest possible confidence interval, max c, for which this difference is significant?
- __________________ Where was Duke Paoa Kahanamoku born?
- __________________ In what sport did Duke Kahanamoku win a gold medal in the 1912 Olympics?
- __________________ 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 | t_{c} | =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 |