The 106 students who were deficient in ESL classes this fall at the national campus had a sample mean x number of deficiencies of 1.68 with a standard deviation of 0.97. The population mean number of defiencies carried by all deficient students is µ = 1.92. Run a hypothesis test to determine whether the ESL students have a different mean number of deficiencies at a significance level of 5%?

- Write out the null hypothesis:
- Write out the alternate hypothesis:
- _________ What is alpha α?
- _________ How many degrees of freedom are there?
- _________ Determine t
_{c} - _________ Find the t-statistic t.
- Do we:
- ___ Reject the null hypotheis? OR
- ___ Fail to reject the null hypothesis?

- ___________________________ Is the mean number of deficiencies for the ESL students different from the population mean number of deficiencies for deficient students?
- ___________________________ Are the ESL students less deficient that the overall population?
- _________ What is the p-value for this hypothesis test?
- _________ What is the largest possible confidence interval for which this difference is significant?

Statistic or Parameter | Symbol | Equations | Excel |
---|---|---|---|

Hypothesis Testing | |||

Degrees of freedom | df | = n-1 | =COUNT(data)-1 |

Calculate a t-statistic (t) | t | (x - µ)/(sx/sqrt(n)) | |

Calculate t-critical for a two-tailed test | t_{c} |
=TINV(α,df) | |

Calculate a p-value from a t-statistic t | p | = TDIST(ABS(t),df,#tails) |