7/28/2019 Stats Final Note Sheet 2

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EXAM1MATERIAL:Problem 1:

1)Which of the following should not be used to display the distribution of a quantitative variable: Bar Chart

2)Random sample of 200 students and their heights, average height of all students at the U is unknown and denoted by u; the heights of the sample is xbar, median m and standard

dev. S. which is NOT a statistic? Anything with u, eg. Xbar- u.

3) For two events A and B, P(A)=0.4 and P(B)=0.3, P(A intersect B): A and B are disjoint but not independent.

Problem 2: Probability and Venn Diagram

Let A be the event that people own a cell phone. Let B be the event that people own a pager. P(A) = 0.72 P(B) =

0.38 P (A B) = 0.29

(a) Probability that a randomly selected person owns a cell phone or a pager or both is P (A B).P (A UB) = P (A) + P (B) P (A B) = 0.72 + 0.38 0.29 = 0.81

(b) Probability that a randomly selected person from this city owns a cell phone but no pager is all that is in A but not in B

= P (A) P (A B) = 0.72 0.29 = 0.43

(c) Conditional probability that a randomly selected person owns a pager given they own a cell phone is the probability of B

given A. P(B|A)= P(BA) = 0.29 =0.40

Problem 3: Tree Diagram, Conditional Prob.

(a) Tree diagram is

(b) Probability that the womens pregnancy is positive P (+) = 0.2475 + 0.015 = 0.2625

(c) Probability that the woman is pregnant given that the test is positive. P (Pregnant|+) = P (Pregnant)/P(+) =

0.2475/0.2625= 0.943

Problem 4:Z-score, Percentiles, Prob. Of Data within Range

(a) z= X/ = 6.26.1 /0.4= 0.10/0.4 =0.25

6.2 oz is 1/4th of a standard deviation away from the mean.

(b) We need to find P(6.0[1] 2.404892Problem 4: Two Sided Hypothesis Test

PT1:We are 95% confident that the mean difference

in the political ideology of among Vegetarians and

Non-vegetarians is from 0.20 to 1.72.

PT2: H0 : X1 X2 = 0 Ha : X1 X2 0

FROM R: >qt(p=0.05, df=8, lower.tail=FALSE) >1.859548

Thus, t-test>t-critical: we rejectthe null hypothesis that the difference of

means of political ideology between vegetarians and non-vegetarians is the same.

(c) Type I error would be possible here, since type I error occurs when we reject the null hypothesis when the null hypothesis was actually true. In this case since we rejected thenull hypothesis, if the null hypothesis was true, we would have a type I error. Type II error is not possible here, because for Type II error to occur, we have to accept the null

hypothesis, which we wont do here.