Basic Applied Statistics 200
Solutions to Midterm 2
-
- 4.1+2(0.1)=4.3
- z=(3.88-4.1)/0.1=-2.2
- (iii) because z is between -1.96 and -2.326
-
- (iii) (large enough n ensures Central Limit Theorem applies
- (ii) (pop greater than 10n ensures dependence doesn't undermine
formula for sd)
- PROPORTION has mean p=0.20
- z=(0.23-0.20)/0.05=+0.6
- (i) because z is not unusual
-
- mean of sample means is population mean 0.15; s.d. of sample means is
population s.d. over square root of sample size, or 0.3
- (iii) As we take larger samples, the shape becomes closer to normal.
However, 4 is a small-sized sample, and the distribution is clearly
right-skewed, so sample mean will still have right skewness.
-
- (i) (They reject the null hypothesis that vaccines do not cause autism.)
- (ii) (The court did not reject the null hypothesis.)
-
- (iv) 0.10(150)=15
- (vii) 0.90(150)=135
-
- (ii)
- (iii) (P-value is slightly larger than 0.05, so if we use 0.05 as our
cutoff, we can't quite reject)
- (iii) because the P-value is borderline
- 0.104 (twice the size)
-
- square root of 0.62(1-0.62)/1,042=0.015
- 0.68 plus or minus 2(0.015)= (0.59, 0.65)
- (i) because the multiplier would be less than 2 [not (ii): smaller n
tends to give wider intervals]
- (iii) because 0.36 is way outside the interval
- (ii) [It's making a claim about p, not p-hat, but p does not obey the
laws of probability, so we use the word "confidence".]
-
- (iii) (it's the farthest AWAY FROM 24)
- (i) (it's the farthest BELOW 24)
- (ii) (refer to t because n is small and sigma is unknown)
- (i) (refer to z because n is large; an outlier isn't a problem if n is large)
- (iii) (because sample is not representative)
- (iii) (because standardized sample mean does not follow t distribution
when sample is small and non-normal)
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