Applied Statistical Methods 1000
Solutions to Practice Final
-
- (vi) side-by-side boxplots (comparing values of a quantitative variable
for several groups)
- (iv) scatterplot (looking at the relationship between two quantitative
variables)
- (ii) two-way table (looking at the relationship between two categorical
variables)
- (ii) is matched pairs
- (ii) a 99% confidence interval
-
- (i) z test about a proportion
- (iv) t test about a mean with one-sided alternative
- (vii) two-sample t test with two-sided alternative
- (ii) z test about a mean with one-sided alternative
- (x) inference for regression
- (ix) ANOVA
- (viii) chi square test
-
- (v) +.6 because it is positive and moderate
- -113+36.5(9)=215.5; you should underline s = 75.93
- yes; you should circle the p-value 0.01
- (ii) prediction interval
- (ii) prediction interval
-
- (i) observational study; race and layoffs are not treatments that
would be imposed by researchers
- null hypothesis states no relationship between race and layoffs;
alternative states there IS a relationship
- (i) African Americans (.086 vs. .031 for whites)
- AA and Laid Off: 75.3; AA and Not Laid Off: 1434.7
White and Laid Off: 144.7; White and Not Laid Off: 2755.3
- 39.7+20.7+2.1+1.1 = 63.6
- (2-1)*(2-1) = 1
- P-value < .001, since 63.6 >10.83
- (i) P-value is small, providing evidence of a relationship
- 30.5 plus or minus 2.64 * 4.9/(square root of 81) = (29.1, 31.9)
-
- observational study
- age; quantitative
- ear length; quantitative
- $b_1$ (the observed slope of the regression line which tells how
much the response---ear length---increases for every unit increase of
the explanatory variable---year)(
- ear length
-
- null hypothesis: mu=50; alternative hypothesis: mu>50; t=2;
df=15; p-value between .05 and .025, so YES, there is compelling
evidence that mu>50.
- .10 and .05
- (iii)
- (i) administrators; (ii) students
-
- null hypothesis: means equal for SF and LA; alternative: means not equal
- df is smaller of 14-1 and 16-1, or 13; p-value > 2(.10)=.20 since
alternative is two-sided
- no because the p-value is not small
- no, because samples are small
- circle the StDev's 1.02 and 1.09 (yes, the Rule of Thumb is satisfied)
-
- 1 has highest mean
- 2 has largest standard deviation
-
- (ii)
- yes; circle s1, s2, and s3 or s1 (largest) and s2 (smallest)
- null hypothesis: the three means are equal; alternative hypothesis:
not all three population means are equal
- DFG=2, DFE=15; MSG=145.5, MSE=3.7; F=39.3>6.36; P-value<.01
so we conclude that the mean time is not the same for all 3 groups
- 14,3,10,6,11,16
- (i)
-
- mean = 15; standard deviation = square root of 60*.25*(1-.25) = 3.354
- P(Z>(18-15)/3.354) = .1867
- mean = .25; standard deviation = square root of .25*(1-.25)/60 = .056
- P(Z>.89) = .1867
- no, because the p-value is large
- .3 plus or minus 1.645 times square root of (.3)(1-.3)/60
=.3 plus or minus .1 = (.2, .4)
-
- (i) confounding variables
- observational study; (iv) ANOVA
- .44 plus or minus 1.96 times square root of (.44)(.56)/400
=.44 plus or minus .05 = (.39, .49)(i)
- reject Ho, conclude population proportion with increased desire to
quit is less than .5 (a minority)
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