The two data sets in the table below are dependent random samples. The population of (x−y)(x-y) differences is approximately normally distributed. A claim is made that the mean difference (x−y)(x-y) is greater than 17.9.

For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t =" before your answers. Round each of your answers to 3 places after the decimal point.

(a) Calculate the value of the test statistic used in this test.

     Test statistic's value =

(b) Use your calculator to find the P-value of this test.

     P-value =

(c) Use your calculator to find the critical value(s) used to test this claim at the 0.04 significance level. If there are two critical values, then list them both with a comma between them.

     Critical value(s) =

(d) What is the correct conclusion of this hypothesis test at the 0.04 significance level?     

• There is sufficient evidence to warrant rejection the claim that the mean difference is greater than 17.9
• There is not sufficient evidence to support the claim that the mean difference is greater than 17.9
• There is not sufficient evidence to warrant rejection the claim that the mean difference is greater than 17.9
• There is sufficient evidence to support the claim that the mean difference is greater than 17.9

A survey is conducted using 2000 registered voters who are asked to choose between candidate A and candidate B. Let p denote the fraction of voters in the population who prefer candidate A and let ˆp denote the fraction of voters who prefer Candidate B.

i You are interested in performing the following hypothesis test H0 : p = 0.4 (1) H1 : p 6= 0.4

(2) Determine the size of the test and compute the power of the test if the true value is p = 0.45

ii Assuming that in the survey ˆp = 0.44. Test H0 : p = 0 − 4 vs H1 : p 6= 0.4 using a 10% significance level

iii Assuming that in the survey ˆp = 0.44. Test H0 : p = 0 − 4 vs H1 : p < 0.4 using a 10% significance level

iv Construct a 90% confidence interval for p

iv Construct a 95% confidence interval for p iv Construct a 99% confidence interval for p

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 11, 9, 4, 6, 6. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.) s = (b) Multiply each data value by 7 to obtain the new data set 77, 63, 28, 42, 42. Compute s. (Round your answer to one decimal place.) s =

For this discussion, comment on any programming errors you encountered.

Did the same issues keep recurring?

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.