Basic Applied Statistics 200
Solutions to MIDTERM 2
-
- 10.4-2(4.6)=1.2 to 10.4+2(4.6)=19.6
- P(X>20)=P(Z>(20-10.4)/4.6)=P(Z>+2.09)=P(Z<-2.09)=.0183
-
- mean of sample means is population mean 100, s.d. of sample means is
population s.d. over square root of sample size, or 10.61
- (iv) shape of distribution of sample mean is still right-skewed
because the sample size (8) is so small
-
- (i) population should be at least 10 times sample size
- (ii) sample must be large enough to use a normal approximation
- COUNT X has mean np=100(.8)=80 and sd square root of np(1-p) = 4.0
- PROPORTION has mean p=.8 and sd square root of p(1-p)/n = .04
- P(sample prop.<.70)=P(Z<(.7-.8)/.04)=P(Z<-2.5)=.0062
- (ii) because of the small probability in (e)
- (i) is the same as rejecting the null hypothesis when it's true
- (i) since Ho was rejected in (f)
- (ii) a statistic called p-hat
-
- (viii) In the long run, 95% of the 200 intervals, or 190, should contain p.
- (iv) In the long run, 5% of the 200 tests, or 10, should reject a true Ho.
-
- .38 plus or minus .03=(.35,.41)
- (ii) narrower
- (i) wider
- (i) yes because .40 is in the interval
- (iii) both are biased: (i) because of a non-representative sample
and (ii) because of a preceding question
- (iii) is the correct interpretation
-
- (vi) is the correct interpretation
- Ho: mu=1 vs. Ha: mu not equal to 1
- t=(1.3-1)/(.5/square root of 15)=2.32
- p-value between 2(.025) and 2(.01): in (.02, .05)
- (i) Since the p-value is small, we reject Ho and conclude there
is convincing evidence that the alternative is true: population mean
number of siblings is not 1.
- .01 to .025
-
- (i) yes: two scores recorded as a pair for each student
- n minus 1 = 17-1=16
- (iii) can't quite reject Ho,
because the p-value is just over .05
- (i) OK because the histogram is roughly bell-shaped
- (ii) the CI just barely includes zero
- (iii) which quiz is taken constitutes the categorical explanatory
variable
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