An athletic footwear company is attempting to estimate the sales that will result from a television advertisement campaign of its new athletic shoe. The contribution to earnings from each pair of shoes sold is $40. Suppose that the probability that a television viewer will watch the advertisement (as opposed to turn his/her attention elsewhere) is 0.40. Furthermore, suppose that 1% of viewers who watch the advertisement on a local television channel will buy a pair of shoes. The company can buy television advertising time in one of the time slots according to Table below:
Television advertising costs and viewers

(a) Suppose that the company decides to buy one minute of advertising time. Which time slot would yield the highest expected contribution to earnings net of costs? What is the total expected contribution to earnings resulting from the advertisement?
(b) Suppose the company decides to buy two one-minute advertisements in different time slots. Which two different time slots should the company purchase to maximize the expected contribution to earnings? What is the total expected contribution to earnings resulting from these two advertisements?

Check in each case whether the given function can serve as the probability distribution of an appropriate random variable. (a) f(x) = (2 x)/4 for x = 0, 1, 2; (b) f(x) = x - 2/9 for x = 1, 2, 3, 4, 5, 6; (c) f(x) = x^2 - 6x + 9/10 for x = 1, 2, 3, 4, 5; (d) f(x) = x^2 - 6x + 8/5 for x = 1, 2, 3, 4, 5.

1. A television CEO believes viewership of the evening news does not depend on age. She collects a random sample of 2000 television viewers across four different age groups and asks whether or not they watch the evening news. The results are as follows:

Watch              | 18 years old             19 to 35             36 to 54            55 years old

Evening News | or less                       years old            years old             or more

___________________________________________________________

Yes                  |           74                        96                                112 146

No                   |           426                      404                              388                  354

Test to see whether watching the evening news and age grouping are independent at the 0.05 level using the Chi-Square test. Conduct this test by hand and using the Chi-Square table instead of using Excel.

The number of wooden sailboats constructed per month in a small shipyard is a random variable that obeys the probability distribution given in Table below: Probability distribution of monthly Number of Sailboats /Probability( 2 is the sailboat and 0.15 is probability; likewise please consider in this way for the rest of the data) 2, 0.15; 3, 0.20; 4, 0.30; 5, 0.25; 6, 0.05; 7,0.05; Suppose that the sailboat builders have fixed monthly costs of $30,000 and an additional construction cost of $4,800 per boat. (a) Compute the mean and standard deviation of the number of boats constructed each month. (b) What is the mean and standard deviation of the monthly cost of the sailboat construction operation? 4 (c) How do your answers in part (b) change if the fixed monthly cost increases from $30,000 to $53,000? Try to compute your answer using the results of the calculation in part (b) only. (d) How do your answers in part (b) change if the construction cost per boat increases from $4,800 to $7,000, but the fixed monthly cost stays at $30,000? Try to compute your answer using the results of the calculations of parts (a) and (b) only.

Thirty-one small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 44.1 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error decreases.As the confidence level increases, the margin of error remains the same.    As the confidence level increases, the margin of error increases.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval increases in length.As the confidence level increases, the confidence interval remains the same length.    As the confidence level increases, the confidence interval decreases in length.

You are drawing 3 cards from a deck of 52.

a) What is the probability you draw an ace of spades, ace of hearts, and an ace of clubs in that order

b) What is the probability you draw 3 aces

c) what is the probability you draw 3 of a kind of any card.

How does data quality affect Business Analytics?

Brand ways Company indicate on the label that their loaves weigh 500g. A sample of 50 loaves is selected hourly from their processing line and the contents weighed. Last hour a sample of 50 loaves had a mean weight of 503g with a standard deviation of 13g. Test at 0.05 significance level whether their process is out of control?

In probability theory, a conditional probability measures the probability of an event given another event has occurred. The conditional probability of A given B, denoted by P(A|B), is defined by P(A|B) = P(A ∩ B) P(B) , provided P(B) > 0. Show that the conditional probability defined above is a probability set function. That is show that a) P(A|B) ≥ 0 [4 Marks] b) P(S|B) = 1. [4 Marks] c) P( S Ai |B) = PP(Ai |B) [4 Marks]

Grades and AM/PM Section of Stats: There were two large sections of statistics this term at State College, an 8:00 (AM) section and a 1:30 (PM) section. The final grades for both sections are summarized in the contingency table below.

Observed Frequencies: O_i's

The Test: Test for a significant dependent relationship between grades and the section of the course. Conduct this test at the 0.05 significance level.

(a) What is the null hypothesis for this test?

H₀: The section (AM/PM) of a course and the grades are independent variables. H₀: The section (AM/PM) of a course and the grades are dependent variables.      

(b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places.

χ²

=  

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀     

(e) Choose the appropriate concluding statement.

We have proven that grades and section of the course are independent.The evidence suggests that there is a significant dependent relationship between grades and the section of the course.     There is not enough evidence to conclude that there is a significant dependent relationship between grades and the section of the course.

A pet food company has a business objective of expanding its product line beyond its current kidney- and shrimp-based cat foots. The company developed two new products, one based on chicken liver and the other based on salmon. The company conducted an experiment to compare the two new products with its two existing ones, as well as a generic beef-based product sold in supermarket chains.

For the experiment, a sample of 50 cats from the population at a local animal shelter was selected. Ten cats were randomly assigned to each of the five products being tested. Each of the cats was then presented with 3 ounces of the selected food in a dish at feeding time. The researchers defined the variable to be measured as the number of ounces of food that the cat consumed within a 10-minute period that began when the filled dish was presented to the cat. The results for this experiment are summarized in CatFood.

a. At the 0.05 level of significance, is there evidence of a differences in the mean amount of food eaten among the various products?

b. Does the result in (a) give you statistical permission to probe for individual differences between the food products?

Please show me how to do this in excel using the data analysis tab

Support of Background Checks by Political Party: In April of 2013, the U.S. Senate did not pass a bill to expand background checks to all gun sales despite popular approval of the idea. Gallup conducted a poll on this issue with the question: Would you vote for or against a law to require background checks for all gun sales?. The results by political affiliation are summarized in the contingency table below.

Observed Frequencies: O_i's

The Test: Test for a dependent relationship between party affiliation and opinion on expanded background checks. Conduct this test at the 0.05 significance level.

(a) What is the null hypothesis for this test?

H₀: Party affiliation and opinion on expanded background checks are independent variables. H₀: Party affiliation and opinion on expanded background checks are dependent variables.      

(b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places.

χ²

=  

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀     

(e) Choose the appropriate concluding statement.

We have proven that opinion on expanded background checks and party affiliation are independent.The evidence suggests that there is a dependent relationship between party affiliation and opinion on expanded background checks.     There is not enough evidence to conclude that party affiliation and opinion on expanded background checks are dependent.

Use the following information to answer the next three questions. Civil engineers collected data from one area of Calgary on the amount of salt (in tons) used to keep highways drivable during a snowstorm. The amount of salt for n=10 snowstorms were as follows: 1111, 2215, 1573, 2813, 2815, 2126, 854, 3965, 1819, 776. Find a 95% confidence interval for the true population mean amount of salt required in a snowstorm.

1) What is the margin of error for this CI?

2) Lower bound ?

3) Upper bound?

Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the z test statistic for the hypothesis test.
A report on the nightly news broadcast stated that 10 out of 108 households with pet dogs were burglarized and 20 out of 208 without pet dogs were burglarized.