Statistics and Probability Answers

Let A and B be two events associated with a statistical experiment, with P(A) = 3 4 , P(B) = 1 2 and P(A ∩ B) = 1 4 . Compute (a) P(A ∪ B) (b) P(A|B) (c) P(B|A) (d) P(A ′ ∩ B ′ ) (e) Are A and B independent events? why? (f) Are A and B mutually exclusive events? why?

. Eight vitamin and six sugar tablets identical in appearance are in a box. One tablet is taken at random and given to Person A. A tablet is then selected and given to Person B. What is the probability that

a.

Person A was given a vitamin tablet?

b.

Person B was given a sugar tablet given that Person A was given a vitamin tablet?

c.

neither was given vitamin tablets?

d.

both were given vitamin tablets?

e.

Person A was given a sugar tablet and Person B was given a vitamin tablet?

f.

Person A was given a vitamin tablet and Person B was given a sugar tablet?

Heights of NBA Players. The average height of an NBA player is 6.698 feet with a standard deviation of 0.45 feet. A random sample of 30 players’ heights from a major college basketball program found the mean height was 6.75 feet. At alpha = 0.05, a researcher wants to determine if there is sufficient evidence to conclude that the mean height differs from 6.698 feet. What is the test value of the study?

Brand Kidzania wanted to study the impact of its brand personality on the customer brand engagement. The five elements of brand personality are Sincerity, Excitement, Competence, Sophistication, Ruggedness. The multiple regression analysis of the data collected is as follows:

personality are Sincerity

Model Summary

Model R R square Adjusted R square std. error of the estimate

1 .928^a .863 .835 3.42991

Anova

Model Sum of squares df mean square F Sig

1 Regression 134.904 5 26.981 2.293 .038^b

Residual 2023.455 172 11.764

Total 2158.360 177

coefficient

Unstandardized standardized

coefficients coefficient

Model B std. error Beta t Sig

1 ( constant) 13.318 1.059 12.577 .000

Sincerity -.226 .118 -2.54 -1.921 .046

Excitement .319 .141 .348 2.267 .025

competence -0.52 .121 -0.59 -415 .679

sophistication .059 .165 .050 357 .722

ruggedness .127 .187 .074 . 687 .499

a. is this model significant ? State the null and alternate hypothesis.

b. which are the independent (IV) and dependent variable (DV)?

c. Which independent variables can be concluded as the predictors of dependent variables and why?

d. what is the percentage of variation explained by independent variable in dependent variable?

e. Write the regression equation

f. interpret the partial regression coefficients.

g. what is the sample size?

A jar contains 8 pennies, 4 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Find the probability X=10

What is the variance of the discrete random variable?

Kai, a seventh grader, wants to determine the average number of times the families in his neighborhood visit the pool during the summer. He samples the families of four of his classmates. Which improvements could Kai make to his sample to increase the validity of the results? Select three choices.

sample more families

sample families that have children who are not in seventh grade

sample families that regularly use the pool

sample families whose answer to the survey question is predetermined

sample families living in every third house in the neighborhood

Determine the critical value of Scheffe’s test if the given value of the problem is K= 5 and N = 20 with 5% level of significance