A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following frequency table:

                                             Number of Children

         If a working woman has more than 2 children, what is the probability she has a low or medium salary?

         A.      0.79            B.      0.45            C.      0.35            D.      0.95

Q 1.An online retailer, Mr Collins Ndhlovu, has two adverts posted in different parts of a well-known social networking website, Advertisement A and Advertisement B. An average of 2 ‘clicks’ are generated by Advertisement A during the period Monday 10.00 to 10.05am. There are on average 5 ‘clicks’ generated by Advertisement B during the same period. Calculate the probability that on a particular Monday between 10.00 and 10.05 am: i)Advertisement A generates at most 3 clicks. ii)Advertisement A generates at least 4 clicks. ii)Advertisement B generates no more than 4 clicks. iv)Advertisement A generates exactly 2 clicks and Advertisement B exactly 2 clicks. v)At least 3 clicks are generated in total by the two advertisements. (5marks)

Explain the difference between a confidence interval and a prediction interval?

The National Association of Home Builders provided data on the cost of the two most popular home remodeling projects. Sample data on cost in thousands of dollars for two types of remodeling projects are as follows.

Using Kitchen as population 1 and Master Bedroom as population 2, develop a point estimate of the difference between the population mean remodeling costs for the two types of projects (to 1 decimal).
$   thousand

Develop a 90% confidence interval for the difference between the two population means (to 1 decimal). Use z-table.
( ,  )

A recent survey reported that 39​% of​ 18- to​ 29-year-olds in a certain country own tablets. Using the binomial​ distribution, complete parts​ (a) through​ (e) below.

a. What is the probability that in the next six​ 18- to​ 29-year-olds surveyed, four will own a​ tablet?

The probability is ? (Type an integer or a decimal. Round to four decimal places as​ needed.)

b. What is the probability that in the next six​ 18- to​ 29-year-olds surveyed, all six will own a​ tablet?

c. What is the probability that in the next six​ 18- to​ 29-year-olds surveyed, at least four will own a​ tablet?

d. What are the mean and standard deviation of the number of​ 18- to​ 29-year-olds who will own a tablet in a survey of​ six?

e. What​ assumption(s) do you need to make in​ (a) through​ (c)?

The computer that controls a bank's automatic teller machine crashes a mean of 0.4 0.4 times per day. What is the probability that, in any seven-day week, the computer will crash less than 4 4 times? Round your answer to four decimal places.

Describe the kind of data that are collected for an independent-measures t-test and the hypotheses that the test evaluates. The key to helping formulate your explanation would be to include the assumptions of this statistical model, the type of sample used in this model, and a statement about the null hypothesis.

Calculate a geometric series

1.For v greater than 0 and less than 1, what is the Sum(v^i) for i = 1 to 100?

2.For v greater than 0 and less than 1, what is the Sum(v^i) for i = 1 to infinity?

3.Let v = 1/(1+r). State the answer to question 2 in terms of r.

Question 1 contains the actual values for 12 periods (listed in order, 1-12). In Excel, create forecasts for periods 6-13 using each of the following methods: 5 period simple moving average; 4 period weighted moving average (0.63, 0.26, 0.08, 0.03); exponential smoothing (alpha = 0.23 and the forecast for period 5 = 53); linear regression with the equation based on all 12 periods; and quadratic regression with the equation based on all 12 periods.  Round all numerical answers to two decimal places.

1. The actual values for 12 periods (shown in order) are:

1. Write up the results from this analysis using APA format. Make sure you include each group mean (and SD) exam score, the correct F stat with the correct degrees of freedom and p-value, decision regarding the null, and the follow-up comparisons (if necessary). Use the example in the SPSS ANOVA lecture to help guide you. [3 points]

1) Suppose that E(Y∣X)=X^2. Then E(Y/X) is equal to which of the following?

a) 1 b) E(X) c) E(X^2) d) E(Y)

2)Var(Y∣X=x) is less than or equal to Var(Y) unless Var(Y)=0. True or False?

8-5 (30) X and Y are independent random variables, and both are normally distributed with mean zero and variance one. Two new random variables. Z and W are defined by Z = X² + Y² , W = X/Y

(14) a). Find f_z.w(z.w)indicating the domains over which it is defined.

(6) b). Are Z and W independent? Explain your answer.

(10) c) Find the marginal densities f_W (w) and f_Z (z) and the domain of each.

Neutropenia is an abnormally low number of neutrophils in the blood. Chemotherapy often reduces the number of neutrphils to a level that makes patients susceptible to fever and infections. G. Bucaneve et al. published a study of such cancer patients in the paper "Levofloxacin to Prevent Bacterial Infection in Patients With Cancer and Neutropenia" (New England Journal of Medicine, Vol. 353, No. 10, pp. 977-987). For the study, 375 patients were randomly assigned to receive a daily dose of levofloxacin, and 363 were given a placebo. In the group receiving levofloxacin, fever was present in 243 patients for the duration of neutropenia, whereas fever was experienced by 308 patients in the placebo group. (Source: Elementary Statistics, Weiss, 8th Edition)

Calculate the margin of error for a 95% confidence interval for the difference in the proportion of patients with fever between patients taking levofloxacin and those not taking anything while suffering from neutropenia. (round proportions to hundredths place, round the critical value to the hundredths place, the standard error to the thousandths place , and the margin of error to the thousandths place)

In clinical tests of adverse reactions to the drug

Viagra, 51 of the 734 subjects in the treat

ment group experienced dyspepsia (indigestion) and

22 of the 725

subjects in the placebo group experienced dyspepsia (based on data from Pfizer Pharmaceuticals). Using a

0.05 significance level, test the claim that the proportion of dyspepsia cases among V

iagra users (group 1)

is greater than the proportion of dyspepsia cases among non

-Viagra users (group 2).

a)

What proportion of Viagra users experienced dyspepsia?

A. 0.030

B. 0.069

C. 0.073

D. 0.050

b) Based on the description above, w

hat

are the

null

and alternative hypothes

es, respectively

?

A.

p

1

=

p

2

,

p

1

≠

p

2

B.

p

1

>

p

2

, p1 < p2

C.

p

1

≤

p

2

,

p

1

>

p

2

D.

p

1

<

p

2

,

p

1

≥

p

2

c)

What is the value of the calculated z test statistic use

d to test the given hypothesis?

A. 0.048

B. 0.59

C. 3.43

D. 11.75

5

d)

What is the

p

-

value (corresponding to your test statistic)?

A. 0.0003

B. 0.05

C. 0.95

D. 0.9997

E. Cannot be determined from the given information

e)

What conclusion should you make based on the given data?

A. Reject H

0

and conclude there is not sufficient evidence to support the claim that dyspepsia occurs at a higher

rate among Viagra users than those who do not use Viagra.

B. Reject H

0

and conclude there is sufficient evidence to support the

claim that dyspepsia occurs at a

higher rate among Viagra users than those who do not use Viagra.

C. Accept H

0

and conclude there is sufficient evidence to support the claim that dyspepsia occurs at a

higher rate among Viagra users than those who do not

use Viagra.

D. Fail to reject H

0

and conclude there is not sufficient evidence to support the claim that dyspepsia

occurs at a higher rate among Viagra users than those who do not use Viagra.

The time taken by an automobile mechanic to complete an oil change is random with mean 29.5 minutes and standard deviation 3 minutes.

a. What is the probability that 50 oil changes take more than 1500 minutes?

b. What is the probability that a mechanic can complete 80 or more oil changes in 40 hours?

c. The mechanic wants to reduce the mean time per oil change so that the probability is 0.99 that 80 or more oil changes can be completed in 40 hours. What does the mean time need to be? Assume the standard deviation remains 3 minutes.