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Exam 2 Preparation Concept Quiz

Exam 2 Preparation Concept Quiz. Statistics in Business.

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Exam 2 Preparation Concept Quiz

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  1. Exam 2 PreparationConcept Quiz Statistics in Business

  2. 1. To investigate an apparent relationship between 2 categorical variables, Al correctly implements a chi-squared independence test. Bo doubled all the counts in Al’s contingency table. How will Al and Bo’s calculated chi-squared stats compare? • Al’s will be higher than Bo’s • Bo’s will be higher than Al’s • They will be equal • One cannot know without the data. Doubling all the counts exactly doubles the calculated chi-squared statistics…resulting in a lower p-value. Distance = (O-E)^2/E.

  3. 2. The mean of a difference of 2 random variables (X1-X2) is the difference in the means (μ1-μ2). The variance of the difference (if X1 and X2 are independent) is… • The difference in the variances (σ12 – σ22) • The sum of the variances (σ12+ σ22) • The average of the variances (σ12 + σ22)/2 • Depends on whether the random variables are normally distributed. The difference is more variable (less predictable), the more variable (less predictable) is X2.

  4. 3. Al gathered n=10 observations of a numerically-scaled variable, and Bo separately gathered n=40. Remarkably (it’s my question) they got identical sample means and sample standard deviations. How do the widths of their 95% confidence intervals for the mean compare? AtoE • Al’s will be ½ the width of Bo’s • Al’s will be < ½ the width of Bo’s • Bo’s will be ½ the width of Al’s • Bo’s will be < ½ the width of Al’s. • It depends on the sample mean and standard deviation. Bo’s “standard error” (s/) will be ½ Al’s…..AND…Bo’s t.inv.2t(0.05,39) will be smaller than Al’s t.inv.2t(0.05,9). This latter fact makes the width of Bo’s Confidence inteval < ½ the width of Al’s.

  5. 4. Al did a one-tailed test. Bo was lazy (he didn’t want to take the time to specify a 1T alternative), and did a 2T test. If they apply their tests to the same data, how will their p-values compare? • Al’s will be always be lower than Bo’s. • Al’s will always be higher than Bo’s. • They will always be equal. • One cannot know without the data. If Al “guesses right” with his Ha, then his p-value will be ½ of Bo’s. If Al “guesses wrong” it is possible his p-value will be higher. (Imagine if Al thought men were shorter, on average, than women.)

  6. 5. Al used a paired t-test because the data came from n matched pairs. Bo loved ANOVA single factor…and applied it to the two-column data set. Which statement best summarizes these two approaches. A-F • Neither test is valid. • Al’s is valid, Bo’s is not. • Bo’s is valid, Al’s is not. • Both are valid, and Al’s is probably better. • Both are valid, and Bo’s is probably better. • Both are valid, and will give identical p-values. Bo’s is equivalent to a two-sample t-test of means. It is valid. But when the data are paired, the paired test is usually better (gives a lower p-value).

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