Quiz 11: Part IV Hypothesis testing • Name:

On the planet Tau Centauri IV-2 the Gnihton corporation produces stegdiws. A stegdiw should be 5 retems long. Allegations arose from customers that Ghihton was producing stegdiws that were too short. An inspector from the Coordinating Council for Clarity in Commerce and Competition (C⁵) collected a random sample n of five stegdiws. The measure of each of the five stegdiws collected is given in the table. Run a hypothesis test to determine whether the five stegdiws could or could not have come from a population of stegdiws with a population mean µ length of 5 retems at a 5% level of significance. Use a population mean µ of 5 retems.

1. _________ What level of measurement is the data?
2. _________ Determine the sample size n.
3. _________ Calculate the sample mean x.
4. _________ Determine the median.
5. _________ Determine the mode.
6. _________ Determine the minimum.
7. _________ Determine the maximum.
8. _________ Calculate the range.
9. _________ Calculate the sample standard deviation sx.
10. _________ Calculate the sample Coefficient of Variation.
11. ________________________________________ Write the null hypothesis in formal statistical format.
12. ________________________________________ Write the alternate hypothesis in formal statistical format.
    α = 0.05.
13. t_c = __________ Determine t_critical.
14. t = __________ Calculate the t-statistic.
15. p = __________ Determine the p-value using the t-distribution.
16. __________ What is the largest confidence interval c for which this difference is statistically significant?
17. ________________________________________ Would we reject the null hypothesis or fail to reject the null hypothesis that the sample mean is statistically significantly different from the population mean at a 5% level of significance?
18. __________ If we reject the null hypothesis, what is the risk of a type I error based on the p-value?
19. __________ Can the C⁵ prove that the Gnihton corporation is producing stegdiws that are too short at a 5% level of confidence?

Hypothesis Testing
Calculate t-critical for a two-tailed test	tc		=TINV(α;df)
Calculate a t-statistic	t		=(x - µ)/(sx/SQRT(n))
Calculate a two-tailed p-value from a t-statistic	p		= TDIST(ABS(t);df;2)