Elementary Statistics
To my question need a good analysis of some statistical questions I've written with excellent explanations for clarity and formatting.
In a recent advertisement, Gillette claimed that their new Crazy Daisy shaver shaves legs smoother, closer, and safer than any other single-blade disposable razor for women.
After shaving each leg with a different razor (Crazy Daisy versus the Lady Bic) according to their own routine, women rated each shaver on smoothness, closeness, and safety. A composite score of those three attributes ranging from 1-10 was used to test for overall average group differences.
Assume the experiment was conducted three different times with three different groups of women. Answer the questions for each experiment using the following output.
Experiment A Experiment B Experiment C
Sample Size 26 26 36
Mean 1 (Gillette) 7.71 6.61 7.01
Stand Dev 1 (Gillette) 1.05 2.35 2.11
Mean 2 (Bic) 5.96 6.44 6.5
Stand Dev 2 (Bic) .37 1.01 1.87
Test statistic (t) 2.15 2.079 2.006
Critical value -2.05, 2.05 2.21 1.87
P-value .041 .12 .0597
Significance level .05 .10 .05
F-test P-value .29 .18 .44
Answer or comment about the following for each experiment.
2. What type of statistical tests were conducted in the experiments? ___________, __________
3. Could a different type of test have been used for the experiments? _____________________
4. What type of variables were used in the study (qualitative or quantitative/discrete or continuous)?
Razor ____________ ____________ Score ____________ ____________
5. What level of measurement were the variables on?
Razor _________________________ Score _________________________
6. Were the samples independent or dependent? __________________________
: Hypothesis Testing
7. What numbers are being compared in the t-test ________________ and the F-test?
__________________ (means, proportions, variances)
8. How many participants were in each study? A_________ B__________ C___________
9. Which number from the output is compared to the significance level to check if the null
hypothesis should have been rejected? _________________________________________
10. Which number from the output gives the probability of a type-I error that is calculated from
the sample data? __________________________________________________________
11. Was a right, left, or two-tailed test run? A ___________ B __________ C __________
12. Would there be a statistically significant difference between the means if the significance
level was set at .10. A __________ B __________ C __________
13. What determines if the variances need to be pooled in the test statistic? _______________
14. Which number from the output shows the pre-determined probability of a type-1 error?
________________________________________________________________________
15. Which number from the output is compared to the critical value to check to see if the null
hypothesis should have been rejected? _________________________________________
16. In each experiment, should the null hypothesis have been accepted or rejected?
A ____________ B _____________ C _____________
17. What type of error (type I or type II) could have been made on experiment?
A_____________ B______________ C_____________
18. In each experiment, was there a statistically-significant difference between the means?
A ____________ B _____________ C _____________
19. What does the F-test test? ___________________________________________________
20. Have the experiments proven that one shaver is better than the other? _____________
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