# Basic Applied Statistics 200 Solutions to Midterm 2

1.
1. .2*.1=.02 (AND means MULTIPLY)
3. (iii) skewed right (sketch a histogram; right tail is longer)
4. 1.76/(square root of 36)=.2933
2.
1. (.90)(50)=45
2. (.10)(50)=5
3.
1. 150/500=.3
2. 125/315=.4
3. (iii)
4. (ii)
5. (v)
4. (b)
5.
1. 30
2. (ii)
3. (i)
4. mean is 30(.65)=19.5; sd is square root of 30(.65)(.35)=2.61
5. P(X>25)=P(Z>(25-19.5)/2.61)=P(Z>2.11)=.0174
6. (i) very unusual because P-value is very small
6.
1. not disjoint, because there is some overlap (males with earrings)
2. 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.
7.
1. Ho:mu=571; Ha: mu not equal to 571 ("Is this significantly different from..." suggests the general, two-sided alternative.)
2. z=(587-571)/(112/square root of 322)=2.56
3. P-value=2P(Z>|2.56|)=2(.0052)=.0104 [I also gave credit if you produced the interval .02 to .01 using Table D.]
4. (ii) .0104 is small
5. (ii) 322 is large
6. .0052 (or the interval from .01 to .005)
8.
1. 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)
2. (i) yes, since 7 is in the interval
3. (v)
4. (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]
9.
1. (i) yes
2. (i) yes definitely, because the P-value .013 is quite small
3. (i) flipping a coin lets order be random