Statistics in a Modern World 800
Solutions to Practice Exam 4
-
- mean of sample proportions is population proportion .5
- standard error is square root of (.5(1-.5)/25) = .1
- shape is normal or bell-shaped
- 68% within .1 of .5: between .4 and .6
- 95% within 2(.1) of .5: between .3 and .7
- 99.7% within 3(.1) of .5: between .2 and .8
- (c) (-.5, 2), because this interval contains zero
- (a) (5,8) and (6,9) have the most overlap
- (b) (5,8) and (9,12) are furthest from each other
-
- 57 plus or minus 2(3)/10 = 57 plus or minus .6 = (56.4, 57.6)
- (i) wider because square root of sample size is in the denominator
of the margin of error
- (iii) unreliable because the sample is not random
- (i) 90% refers to chance of success of the method
- (c) .0549 could be considered a borderline p-value; a larger sample may
yield more conclusive results
- (c) the sample must be random, and there should be at least 5 of each
type of outcome: here there'd be about 8 in the category of interest,
72 not
-
- (ii) null hypothesis states population proportion = .5
- (iii) alternative hypothesis states population proportion > .5
- (i) hypothesized population proportion is used to calculate standard
error
- square root of (.5(1-.5)/49) = .07
- z = (.63 - .50)/.07 = 1.86
- p-value = probability of z > 1.86 = probability of z < -1.86 = .03
- yes, there is convincing evidence that a majority prefer fresh-brewed
- (a) is matched pairs
because 2 measurements are made on the same individuals
- p-value for two-sided test is 2(.03) = .06
- (a)very small p-value means strong evidence of a difference;
it doesn't necessarily mean the difference is large
- (b) Simpson's paradox means a change in the relationship in a two-way
table when tables are combined, so the survival rate would be higher in
hospital B
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