Basic Applied Statistics 200
Solutions to Practice Midterm 2
-
- 30
- (ii)
- (i)
- mean is 30(.65)=19.5; sd is square root of 30(.65)(.35)=2.61
- P(X<5)=P(Z<(5-19.5)/2.61)=P(Z<-5.56)=0 (approximately)
- (i) virtually impossible because P-value is practically zero
- mean is p=.65, standard deviation is square root of (.65)(.35)/30=.087
-
- mean plus or minus 2 sds: between 600 and 1440
- P(X>820)=P(Z>(820-1020)/210)=P(Z>-.95)=P(Z<+.95)=.8289
- top 3% have z=1.88, so x=1020+1.88(210)=1414.8, or 1415
-
- mean is 3.5, sd is 1.7/5=.34
- (x) 90% of 50 is 45
- (ii) 10% of 50 is 5
-
- 16/89=.18
- Ho:p=.20 vs. Ha:p not equal to .20
- z=(.18-.20)/sq rt of (.2)(.8)/89 = .47
- 2P(Z>|.47|)=2P(Z>.47)=2P(Z<-.47)=2(.3192)=.6384
- (ii) large P-value means no reason to reject Ho
- .18 plus or minus 2 times square root of .18(.82)/89
=.18 plus or minus .08 = (.10, .26)[You can also multiply by 1.96 instead
of 2, but after rounding, the interval will be the same.]
- conservative margin of error is m=1/sq rt of n, so n=1/m squared=
1/(.10)(.10)=100
-
- Note that sample size is small, so this should
be a t confidence interval, not z. There are 15 degrees of freedom.
CI is 7.1 plus or minus 2.95(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]
- (b)
- Note: The problem statement should have presented 112 as sample
standard deviation, not population standard deviation. Please fix
this error on your practice exam.
- Ho:mu=571; Ha: mu not equal to 571 ("Is this significantly different
from..." suggests the general, two-sided alternative.)
- t=(611-571)/(112/square root of 36)=2.14
- df = 36-1 = 35; use 30 df in Table A.2 (safer than 40)
- for 30 df, 2.14 is between 2.04 and 2.46, so the P-value is between
2(.025) and 2(.01); between .05 and .02
- (ii) from (d), P-value is smaller than alpha = .05 so we reject Ho
and conclude Ha is true: mean math SAT differs from 571
- (iii)
- between .025 and .01
-
- (i) parameter
- (iii) parameter
- (ii) statistic
- (iv) statistic
-
- (i) yes
- (i) yes definitely, because the P-value .013 is quite small
- (i) flipping a coin lets order be random
-
- (ii)
- (i)
-
- (i)
- (ii)
- (a)
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