### MS 150 Stat Q10 Fall 2005 p-value • Name: _______________

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%?

1. Write out the null hypothesis:
2. Write out the alternate hypothesis:
3. _________ What is alpha α?
4. _________ How many degrees of freedom are there?
5. _________ Determine tc
6. _________ Find the t-statistic t.
7. Do we:
1. ___ Reject the null hypotheis? OR
2. ___ Fail to reject the null hypothesis?

8. ___________________________ Is the mean number of deficiencies for the ESL students different from the population mean number of deficiencies for deficient students?
9. ___________________________ Are the ESL students less deficient that the overall population?
10. _________ What is the p-value for this hypothesis test?
11. _________ 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 tc =TINV(α,df)
Calculate a p-value from a t-statistic t p = TDIST(ABS(t),df,#tails)