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.
- _________ What level of measurement is the data?
- _________ Determine the sample size n.
- _________ Calculate the sample mean
- _________ Determine the median.
- _________ Determine the mode.
- _________ Determine the minimum.
- _________ Determine the maximum.
- _________ Calculate the range.
- _________ Calculate the sample standard deviation sx.
- _________ Calculate the sample Coefficient of Variation.
- ________________________________________ Write the null hypothesis in formal statistical format.
- ________________________________________ Write the alternate hypothesis in formal statistical format.
α = 0.05.
- tc = __________ Determine tcritical.
- t = __________ Calculate the t-statistic.
- p = __________ Determine the p-value using the t-distribution.
- __________ What is the largest confidence interval c for which this difference is statistically significant?
- ________________________________________ 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?
- __________ If we reject the null hypothesis, what is the risk of a type I error based on the p-value?
- __________ Can the C5 prove that the Gnihton corporation is producing stegdiws that are too short at a 5% level of confidence?
|Calculate t-critical for a two-tailed test
|Calculate a t-statistic
||=(x - µ)/(sx/SQRT(n))
|Calculate a two-tailed p-value from a t-statistic||p||