In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in television ads in the United States and the United Kingdom. They found that a substantially greater percentage of U.K. ads use humor.

(a) Suppose that a random sample of 387 television ads in the United Kingdom reveals that 131 of these ads use humor. Find a point estimate of and a 95 percent confidence interval for the proportion of all U.K. television ads that use humor. (Round your answers to 3 decimal places.)   

(b) Suppose a random sample of 493 television ads in the United States reveals that 134 of these ads use humor. Find a point estimate of and a 95 percent confidence interval for the proportion of all U.S. television ads that use humor. (Round your answers to 3 decimal places.)

(c) Do the confidence intervals you computed in parts a and b suggest that a greater percentage of U.K. ads use humor?

(Click to select)YesNo , the U.K. 95 percent confidence interval is (Click to select)not aboveabove the maximum value
in the confidence interval for the U.S.

Briefly explain specifically why categorical and quantitative variables require different methods in order to describe their distributions.

A correct answer will accurately address BOTH types of variables and clearly explain the REASONS these two types of variables REQUIRE different methods.

• Be sure to address WHY the methods differ not just WHAT methods are used in each case.

street performer offers you a chance to play his game for the low price of $10.

His game involves you pushing two different buttons. One of the buttons, when pushed, has a 10% chance of winning you $40;

and the oth er button, when pushed, has a 20% chance of winning you $25. You are allowed two button presses( e ither pushing the same button twice or pushing each button once) in a single game.

Is it worth playing?

1. Liv attends “Happy Days” preschool. The preschool ran assessments on the children’s motor skills (such as ability to tie a shoe), social skills (such as sharing and saying “please” and “thank you”), and school readiness (such as knowing ABCs and basic counting). The motor skills test has a class mean of 6 with a standard deviation of 1, the social skills test has a class mean of 10 with a standard deviation of 2, and the school readiness test has a mean of 16 with a standard deviation of 4. Liv’s parents are given a report that indicates that her z score for motor skills is –1.11, for social skills it is 0.25, and for school readiness it is 0.

a. The parents do not know what z scores are. Clearly define for them what a z score measures and the advantages of using z scores compared to raw scores.

b. What does a z score = –1.11 mean? A z score of 0.25? A z score of 0?

c. What are Liv’s raw scores on each test?

1. ****NEED TO KNOW HOW PROBLEM IS SET UP IN EXCEL***
2. During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.
   1. Clearly state what the random variable in this problem is?
   2. What is an appropriate distribution to be used for this problem and why?
   3. What is the expected number of calls in one hour?
   4. What is the probability of receiving three calls in five minutes?
   5. What is the probability of receiving NO calls in a 10-minute period?
   6. What is the probability of receiving more than five calls in a 10-minute period?
   7. What is the probability of receiving less than seven calls in 15-minutes?
   8. What is the probability of receiving at least three but no more than 10 calls in 12 minutes?

b.The lead engineer on the design team has requested that you match the reliability of the parallel system with a series system. All three of the valves in series will have the same probability of functioning correctly. What does this probability need to be to equal the probability of the parallel system?

c. Comment on the advantages and disadvantages of using parallel systems in aircraft design.

Based on the experimental data, it was determined that the probability of the three valves functioning correctly are:

Valve 1: 95% • Valve 2: 94% • Valve 3: 92%

Problem 4-11 (Algorithmic)

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows:

If the Edwards production plan for the next period includes 1025 units of component 1 and 825 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? Round your answers to the nearest whole number. If your answer is zero, enter "0".

What is the total purchase cost for the components? Round your answer to the nearest dollar.

$ ____________

Please answer the following questions based on the analysis in excel.

1. Calculate the mean, standard deviation, and variance of the two samples. Embed the answers in the data sheet.

2. Calculate the degrees of freedom for a t test assuming the population standard deviation is unknown with unequal variance between samples.

3. Perform a two-tailed two-sample mean test assuming the population standard deviation is unknown with unequal variance. (.01 significance level)

4. State your conclusion from the two-tailed test.

In Texas Hold’em, each player is dealt two cards from the deck. Obviously, this is done without replacement, so you cannot use the binomial distribution. You can use the hypergeometric distribution or reason from first principles.

a) What is the probability of being dealt a pair? Express it as an exact fraction and an approximate percentage.

b) If you are dealt two unpaired cards, say the ace of clubs and the 8 of diamonds, what is the chance of getting a pair or better on the flop? The flop is three cards dealt all at once, and we want to know the chance that the flop will contain at least one ace or at least one 8.

3. You also have been asked to determine at both the 2% and 5% levels of significance whether the proportion of supporters of the candidate that describes itself as generally loyal to the political party of the candidate has decreased recently from its previously hypothesized value of 80%. You select a random sample of supporters of the candidate for study. The sample data concerning whether the supporters generally describe themselves as party loyalists is shown below. Answer the question as to whether there has been a decrease in the population proportion of supporters that describes itself as party loyalists from its previous value of 80%.

Appendix Two: Party Loyalist? (Y = yes, N = no)

Y         Y         Y         N         Y         N         Y         N         Y         N         Y

N         Y         Y         Y         Y         Y         N         N         N         Y         Y

Y         Y         Y         Y         Y         Y         Y         Y         Y         Y         Y

N         Y         N         N         Y         N         Y         Y         N         Y         N

Y         N         N         N         Y         Y         Y         N         Y         Y         N

One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting this disease. A family has three children. The probability of this family having one child who inherited this genetic disease is:

The risk of HIV:

The risk of HIV runs high in North America. In the at-risk population, about 1 in 30 people are HIV carriers, while in general population (people who are not at risk), 1 in 300 are. The at-risk population is 2% in total in North America. Doctors have developed a test for HIV and suppose that it correctly identifies carriers 95% of the time, while it correctly identifies the disease-free only 90%. As the test detects HIV only, you can assume that it is conditionally independent of being at risk, given carrier or not-carrier status.

a. If a random person is sampled, what is the probability that he/she is a carrier?

b. Given that a person has a positive test result and is not in the at-risk population, what is the probability that he/she is a carrier?

How would bias impact developing of accurate predictive models? How would you minimize the impact of bias?

Hypotheses can be written as questions, statements and equality/inequalities. To be truly proficient, you must be able to interpret a hypothesis, regardless of how it is expressed.