Basic Applied Statistics 200
Solutions to Practice Midterm 2
-
- 130+3(20)=190
- P(X>160)=P(Z>(160-130)/20)=P(Z>+1.5)=P(Z<-1.5)=.0668
- Half of a normal variable's values fall below the mean: 130
[or take .5 is the probability of being below z=0 and unstandardize
to 130+0(20)=130]
-
- mean of sample means is population mean 7, s.d. of sample means is
population s.d. over square root of sample size, or 1.67
- (iv) shape of distribution of sample mean is not necessarily normal
because the sample size (5) is so small
-
- (ii) binomial model
- (i) a normal approximation
- COUNT X has mean np=225(.10)=22.5 and sd square root of np(1-p) = 4.5
- P(X>37)=P(Z>(37-22.5)/4.5)=P(Z>3.22)=P(Z<-3.22)=.0006
- (ii) because of the small probability in (d)
- (iii) a parameter called p
-
- 45/75=.6
- Ho:p=.25 vs. Ha:p>.25
- sd is square root of (.75*.25)/75 and z=(.60-.25)/sd=7
- P(Z>7)=0, approximately
- Since the p-value is extremely small, we reject Ho and conclude there
is convincing evidence that the alternative is true: population proportion
recovering with bat saliva treatment is significantly higher than usual
(answer is (i) yes)
- Circle (ii) so subjects are blind, (iii) so there is a control group,
and (v) so researchers are blind
-
- 14.7 plus or minus 2.90(6)/3=(8.9, 20.5)
- (i) is the correct interpretation
- Ho: mu = 11.3 vs. Ha: mu > 11.3
- t=(14.7-11.3)/(6/square root of 9)=1.7
- For 8 df, 1.7 < 1.86 so P-value > .05 [Note: you must give a RANGE
for the p-value for this and for part (f); it's important to know HOW the
p-value compares to .05---whether it is smaller or larger.]
- (iv) the p-value is rather close to .05; more conclusive results
may have been obtained from a larger sample [but I gave partial credit for
(ii)]
- greater than 2(.05)=.10
-
- In the long run, 99% of the 100 intervals, or 99, should contain p.
- In the long run, 1% of the 100 tests, or 1, should reject a true Ho.
- (iii) assume p=.5, p-value is probability of sample proportion less
than or equal to .35
-
- (ii) gives them more conviction
- (i) gives them more precision
- (iii) it depends
-
- (ii) no, it was a two-sample study
- smaller n minus 1 = 10-1=9
- (i) we definitely reject the null hypothesis of equal times,
because the p-value is close to zero
- (ii) maybe incorrect because of small samples
- (iii) one quantitative (times served) and one categorical (fraud or
firearms)
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