Basic Applied Statistics 200
Solutions to Midterm 2
-
- .2*.1=.02 (AND means MULTIPLY)
- .35+.35=.70 (OR means ADD)
- (iii) skewed right (sketch a histogram; right tail is longer)
- 1.76/(square root of 36)=.2933
-
- (.90)(50)=45
- (.10)(50)=5
-
- 150/500=.3
- 125/315=.4
- (iii)
- (ii)
- (v)
- (b)
-
- 30
- (ii)
- (i)
- mean is 30(.65)=19.5; sd is square root of 30(.65)(.35)=2.61
- P(X>25)=P(Z>(25-19.5)/2.61)=P(Z>2.11)=.0174
- (i) very unusual because P-value is very small
-
- not disjoint, because there is some overlap (males with earrings)
- not independent, because knowing whether or not one event occurred
gives us information about the probability of the other. For example, if
I picked a student at random and told you the student had pierced ears,
you would know the student is more likely to be a female.
-
- Ho:mu=571; Ha: mu not equal to 571 ("Is this significantly different
from..." suggests the general, two-sided alternative.)
- z=(587-571)/(112/square root of 322)=2.56
- P-value=2P(Z>|2.56|)=2(.0052)=.0104 [I also gave credit if you
produced the interval .02 to .01 using Table D.]
- (ii) .0104 is small
- (ii) 322 is large
- .0052 (or the interval from .01 to .005)
-
- Note that standard deviation comes from the sample, so this should
be a t confidence interval, not z. There are 15 degrees of freedom.
CI is 7.1 plus or minus 2.947(1.56)/square root of 16=7.1 plus or minus
1.15=(5.95,8.25)
- (i) yes, since 7 is in the interval
- (v)
- (i) reducing C reduces t* which makes the interval narrower;
(iii) larger n leads to a narrower interval [larger sigma means s would
tend to be larger, too, which results in a wider interval]
-
- (i) yes
- (i) yes definitely, because the P-value .013 is quite small
- (i) flipping a coin lets order be random
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