Basic Applied Statistics 200
Solutions to Midterm 2 Fall 2002
-
- NO HIGHER THAN 2 means 0, 1, or 2: add the probabilities to get
.10+.10+.25=.45
- (i) Sketch a quick histogram with bars of height .1, .1, .25,.3, and .25
to see that the distribution is skewed left (has a long left tail)
-
- distribution of sample mean has mean equal to population mean (210),
standard deviation equal to population standard deviation divided by square
root of sample size (25/9=3.57) and shape approximately normal because (ii)
the population is normal, according to the problem statement
- P(X-bar>220)=P(Z>(220-210)/3.57)=P(Z>2.8)=P(Z<-2.8)=.0026
-
- (iii) 2 categorical variables: age here is treated as categorical,
not quantitative
- P(G)=660/6000=.11
- P(G|Y)=210/1500=.14
- (i) more likely, since the answer to (b) is larger than the answer to (a)
-
- (i) .56 is a parameter because it describes the population (all American
adults; .61 describes the sample). LI>
- mean is np=1600(.56)=896,
standard deviation is square root of np(1-p), or square root of 1600(.56)(.44)
=19.86
- P(X>976)=P(Z>(976-896)/19.86)=P(Z>4.03)=0, approximately
- (ii) some were not telling the truth; the discrepancy can't be attributed
to chance variation
- (iii) both a high level of confidence and a narrow interval are desirable
-
- (x) 95% of 100 = 95
- (i) .05 of 100 = 5
-
- 5.15 plus or minus 1.96(1.69)/square root of 4356= (5.1,5.2)
- YES, we anticipate the test to reject Ho:mu=5.0, because 5.0 is NOT
in the above interval.
- (iv) is the only correct choice
- (ii) Yes, because the sample size is large: 4356 is huge enough to
render sample mean normal for any population shape.
- (iv) skewed right; occasionally students take much more time to
graduate.
-
- Ha: mu > 0
- For 16-1=15 df, 3.43 is between two critical values that have
p between .0025 and .001
- (ii) The P-value is very small, providing very strong evidence against
Ho.
- If 2.1 had been sigma instead of s, we would have had a z distribution
instead of t, and could look up the probability in Table A: .0003
- (a) is matched pairs; two height values recorded for each individual
-
- (ii) NO, not at all; a p-value of .46 isn't even close to being small.
- circle the p-value of .46
- one-sided P-value is half the two-sided P-value: 1/2(.46)=.23
-
- (ii) fail to reject Ho even when it is false (small n leads to small
test statistic which leads to large p-value)
- (i) find a statistically significant difference (large n leads to large
test statistic which leads to small p-value)
[ Home
| Calendar
| Assignments
| Handouts
]
|