A corporation only recruits applications who attended one of three schools: College A, B and C. The director HR knows that 10% of the job applicants attended A, 30% attended B and the rest attended C. However 60% of all applicants from A, are offered positions in the Corporation, whereas only 35% of applicants from B and 25% of applicants from C are given offers.

i) What percentage of offer letters go to applicants from College A?

ii) What percentage of offer letters go to applicants from College B?

iii) What percentage of offer letters go to applicants from College C?

The following data are the ages (in years) at diagnosis for 20 patients under treatment for meningitis: 18 18 25 19 23 20 69 18 21 18

20 18 18 20 18 19 28 17 18 18

(a) . Calculate and interpret the values of the sample mean, variance, and standard deviation.

(b) . Compute the sample median. Why might you recommend it as a measure of centre rather than the sample mean? 2

(c) . Compute the upper fourth, the lower fourth, and the fourth spread. (d) . Illustrate the center, spread, and symmetry or skewness of this data using a horizontal modified boxplot.

Anyone who has studied statistics or research has heard the saying "Correlation does not imply causation." What factors must an analyst consider to decide whether the correlation is meaningful enough to investigate further?

annual income for Americans in 2012. Use the data set to answer the following questions: Hint: Use Excel

Data set

income (in dollars)

1. Formulate the null and alternative hypotheses that can be used to test the assumption that the average American annual income is $42,500.

Ho = 42500

Ha ≠ 42500

2. Compute the value of the test statistic.
3. What is the p-value?
4. At α = .05, what is the critical value?
5. At α = .05, what is your conclusion? Briefly justify your answer.
6. Compute a 95% confidence interval for the population mean. Does it support your conclusion?

1. It is believed that the population proportion of adults in the US who own dogs is 0.65. I surveyed people leaving the veterinarians office and found that 96 out of 150 owned a dog. Test this hypothesis at the .05 significance level. Assume a random sample.

2. Randomly surveyed 10 employees at work for their average on how many times they use the rest room per shift. the results were as follows 2,2,3,1,0,4,1,1,0,5

the mean for this is 1.9 times per shift.

test the hypothesis at a .5 significance level.

3.  In the company there are 845 employees who use laptops within the organization. In our office downtown in the city, there are 75 employees who use laptops, walking around in our downtown office there are 55 mac users and 20 dell users. Test this hypothesis with this random sample.

The following table represents the percentage of voters, by age, who favor increasing the minimum wage in a particular city.

Ages 18 - 29 30 - 39 40 - 49 50 - 59 60 and up Percentage 70% 30% 35% 15% 20%

a) Would a pie chart be appropriate for this data? Explain why or why not.

b) Would a Pareto chart be appropriate for this data? Explain why or why not.

QUESTION SEVEN a) A cigarette manufacturing firm distributes two brands of cigarettes. Two random samples are selected and it is found that 56 of 200 smokers prefer brand Α and that 29 of 150 smokers prefer brandΒ . Can we conclude at the 0.05 level of significance that the percentage of smokers who prefer brand Α exceeds that of brand Β by more than 10%?

b) An auditor claims that 10% of invoices for a certain company are incorrect. To test this claim a random sample of 200 invoices are checked and 24 are found to be incorrect. Test at the 1% significant level to see if the auditor’s claim is supported by the sample evidence.

c) The personnel department of a company developed an aptitude test for screening potential employees. The person who devised the test asserted that the mean mark attained would be 100. The following results were obtained with a random sample of applicants:

x = 96,   s= 5.2,   n=13

Test this hypothesis against the alternative that the mean mark is less than 100, at the 1% significance level.

According to recent studies, 57.6% of American citizens are overweight. Suppose that 17% of those who are overweight are children. If American citizen is randomly selected, determine the following probabilities:

a) Selected citizen is overweight and a child

b) Selected citizen is not a child given that he/she is overweight

c) Selected citizen is not a child and is not overweight

The City Council wants to gather input from residents about the recreational opportunities in the city. Categorize each technique as simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample.

a) Get an alphabetical list of all residents and question every 250th resident on the list.

b) Have 10 volunteers go downtown on Saturday afternoon and question people that they see. The volunteers may quit when they have questioned 25 people.

c) Get an alphabetical list of all residents and use a random number to get a sample of 3000 residents to question.

d) Divide the town into 25 distinct geographical neighborhoods then randomly choose 50 residents in each neighborhood to question.

e) Divide the town into 25 distinct geographical neighborhoods then randomly choose 10 of the neighborhoods. Question all the residents in the chosen neighborhoods

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond).

For the past several years, we have the following data

x: 17,0,20,35,37,33,26,−15,−24,−22

y: 20,−10,8,18,19,11,18,−8,−5,−4

(a) Compute ∑x, ∑x2, ∑y, ∑y2

(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y.

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. Use the intervals to compare the two funds.

(d) Compute the coefficient of variation for each fund. Use the coefficients of variation to compare the two funds. If s represents risks and image from custom entry tool represents expected return, then image from custom entry tool can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain.

how does the logistic regression work to further the ability of the results

In the SPSS system exactly what is the variable measure for abany?

How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars).

Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the four types of companies? Use a 5% level of significance.

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 3 decimal places for MS_BET, and MS_W.)

Find the value of the sample F statistic. (Use 3 decimal places.)


What are the degrees of freedom?
(numerator)=
(denominator)=

(f) Make a summary table for your ANOVA test.

We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.

Each card will have:
i) One rank from 1 to 16.
ii) One of 5 different suits.

Hence, there are 80 cards in the deck with 16 ranks for each of the 5 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!

The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get.

e) How many different ways are there to get exactly 3 of a kind (i.e. 3 cards with the same rank)?
The number of ways of getting exactly 3 of a kind is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 3 of a kind?
Round your answer to 7 decimal places.

f) How many different ways are there to get exactly 4 of a kind (i.e. 4 cards with the same rank)?
The number of ways of getting exactly 4 of a kind is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 4 of a kind?
Round your answer to 7 decimal places.

g) How many different ways are there to get a full house (i.e. 3 of a kind and a pair, but not all 5 cards the same rank)?
The number of ways of getting a full house is
DO NOT USE ANY COMMAS

What is the probability of being dealt a full house?
Round your answer to 7 decimal places.


h) How many different ways are there to get a straight flush (cards go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 14, 15, 16, 1, 2)?
The number of ways of getting a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a straight flush?
Round your answer to 7 decimal places.


i) How many different ways are there to get a flush (all cards have the same suit, but they don't form a straight)?
Hint: Find all flush hands and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a flush that is not a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a flush that is not a straight flush?
Round your answer to 7 decimal places.


j) How many different ways are there to get a straight that is not a straight flush (again, a straight flush has cards that go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 14, 15, 16, 1, 2)?
Hint: Find all possible straights and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a straight that is not a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a straight that is not a straight flush?
Round your answer to 7 decimal places.