Discussion:
Q1. Which hypothesis testing model would be used under each of the following conditions. Use the "model number" from my handout if you wish. By line the information given in each cell is: Level of measurement, number of groups, sample size to be taken, parameter of interest and any qualifications.
Conditions Model
Ratio data
One group
Large sample
Population mean
Don't know sigma
Ratio data
Two groups
Large sample
Population means
Populations are normally distributed
Don't know sigmas but assume they are equal
Ratio data
Two groups
Large sample
Test for proportions
Ration data
Four groups
Large sample
Test for equality/inequality of means
Q2. Prove that a population mean is not 150. Use an alpha of 5% and set up the full, detailed, five step hypothesis test. Assume when the sample 201 is taken the sample mean is 151.77 and the sample standard deviation is 10. Use the full 5-step formal hypothesis testing structure. Estimate the p value?
Q3. Test to see if four population means are the same or different. Assume the populations are normally distributed and have equal variances. Use the formal hypothesis-testing model. State the conclusion in statistical terms and in conversational English. Use the ANOVA table below. Determine what the F-critical value is using an αof 5%.
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 900 3 300 3.00 0.0480
Within Groups 2500 25 100
Total 3300