Stat 11 Spring 2011 - Homework 8
(1) Microsoft Excel is a spreadsheet program that also does some statistical calculations. Unfortunately, while Excel's spreadsheet functions are well designed, its statistics routines are sometimes questionable. Furthermore, the online help for statistics functions is sometimes poorly written or incorrect. Below is the online help for the two-sample t-test function:
This analysis tool and its formulas perform a two-sample student's t-test...You can use a t-test to determine whether two sample means are equal. Use this test when the groups under study are distinct. Use a paired test when there is one group before and after a treatment.
What major conceptual error does the author make about the purpose of the two-sample t-test? Explain briefly. (One or two sentences should suffice.)
(2) Some astrologers have speculated that people born under "water signs" are more neurotic than people born under other signs ("Self-Attribution Theory and the Sun-Sign" in Journal of Social Psychology, 1984). A standard personality test (the Eysenck Personality Inventory) was given to samples of subjects born under various signs. The results are given below:
|
|
sample size
|
sample mean neuroticism score
|
sample SD of neuroticism scores
|
|
water signs
|
59
|
12.32
|
4.15
|
|
other signs
|
186
|
12.23
|
4.11
|
Do these data support the claim that those born under water signs differ significantly in neuroticism from those born under other signs? Perform a 2-sided hypothesis test.
(3) Using the data in question (2), calculate a 95% confidence interval for the true mean difference in neuroticism between people born under water signs and people born under other signs. Be sure to use the correct t multiplier in calculating the margin of error. Is your conclusion in question (4) consistent with your confidence interval?
(4) Watch this video of a talk by author Malcolm Gladwell on spaghetti sauce:
https://www.ted.com/talks/malcolm_gladwell_on_spaghetti_sauce.html
I have stated several times in class that although people often focus on the mean, the spread or variation is often as or more important than the mean. Briefly describe how Gladwell's message supports my statement. A few sentences should suffice.
(Optional: You might also watch the talk by Swarthmore professor Barry Schwartz, which is linked from the web page and presents a different viewpoint.)