A used car dealer says that the mean price of a​ three-year-old sports utility vehicle is ​$ 22 comma 000 22,000. You suspect this claim is incorrect and find that a random sample of 22 22 similar vehicles has a mean price of ​$ 22 comma 668 22,668 and a standard deviation of ​$ 1919 1919. Is there enough evidence to reject the claim at alpha α equals = 0.05 0.05​? Complete parts​ (a) through​ (e) below. Assume the population is normally distributed. ​(a) Write the claim mathematically and identify Upper H 0 H0 and Upper H Subscript a Ha. Which of the following correctly states Upper H 0 H0 and Upper H Subscript a Ha​? A. Upper H 0 H0​: mu μ equals =​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ less than <​$ 22 comma 000 22,000 B. Upper H 0 H0​: mu μ greater than or equals ≥​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ less than <​$ 22 comma 000 22,000 C. Upper H 0 H0​: mu μ equals =​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ greater than >​$ 22 comma 000 22,000 D. Upper H 0 H0​: mu μ not equals ≠​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ equals =​$ 22 comma 000 22,000 E. Upper H 0 H0​: mu μ equals =​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ not equals ≠​$ 22 comma 000 22,000 F. Upper H 0 H0​: mu μ greater than >​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ less than or equals ≤​$ 22 comma 000 22,000 ​(b) Find the critical​ value(s) and identify the rejection​ region(s). What​ is(are) the critical​ value(s), t 0 t0​? t 0 t0 equals = nothing ​(Use a comma to separate answers as needed. Round to three decimal places as​ needed.) Determine the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) within your choice. ​(Round to three decimal places as​ needed.) A. nothing less than nothing C. t less than < nothing D. t less than < nothing and t greater than > nothing ​(c) Find the standardized test statistic t. t equals = nothing ​(Round to two decimal places as​ needed.) ​(d) Decide whether to reject or fail to reject the null hypothesis.

A researcher conducts an experiment to compare the effectiveness of different therapies for depression. Participants diagnosed with depression are randomly assigned to one of four groups: Control (no therapy provided), antidepressant medication (SSRI), cognitive-behavioral therapy (CBT), or a combination of medication and cognitive-behavioral therapy (SSRI+CBT). The DV is depression severity after 4 weeks, with higher scores indicating the presence of more depressive symptoms.

Is there a statistically significant difference between the groups? With α = .05, perform a oneway between groups ANOVA to find out.

a. Perform the ANOVA in Excel by creating your own formulas and with the FDIST function to determine p. Create your own full summary table.

b. Compute the effect size (eta squared).

c. Create either a bar graph comparing the means of the four groups (including standard error bars) or a box-plot display comparing the four groups.

d. Insert a textbox reporting your statistical and research conclusion.

A system is composed of five components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector (x1, x2, x3, x4, x5) where xi is equal to 1 if component i is working and is equal to 0 if component i has failed. Suppose that two components are working and three components have failed. In how many ways can this occur?

Although union and non union wages tend to rise at the same rate in the long run, union wages usually advance faster during recessions and early in period of recovery, and non union wages tend to advance more rapidly later in the business cycle when the labor markets are tight. To examine this issue, an economist records the hourly wages (including employee benefits) of employees with two years experience for twelve chosen consumer products manufacturing firms. Six non union shops and six consumer manufacturing firms with union shops. The data (in dollars) are as follows:

Non union shops: 8.26, 8.17, 8.45, 9.09, 8.85, 8.31

Union shops: 7.92, 8.39, 8.64, 8.04, 8.24, 8.25

A) At 5% level of significance, does the data suggest that the union and non-union wages differ, on the average, for employees with two years experience in the consumer products manufacturing industry? Show all necessary work.

B) What type of error is possible and describe this error in terms of the problem?

C) Estimate the difference between the actual average wages of union and non-union employees with two years experience in the consumer products manufacturing industry using a 90% confidence interval. Does the data suggest that there is sufficient evidence of a difference in the actual average wage of union and non-union employees with 2 years experience in the consumer products manufacturing industry? Show all necessary work.

D) Interpret the interval estimation.

The dataset gives the dried weight in pounds of three groups of 10 batches of plants, where each group of 10 batches received a different treatment. The Weight variable gives the weight of the batch and the Groups variable gives the treatment received.

A.) Conduct an analysis of variance to test the hypothesis of no difference in the weights of the plants under different treatments.

B.) Plot and analyze the residuals from the study and comment on model adequacy (All tests are to be performed at α = 0.05)

An engineering group needs to set up an assembly line to produce a new product. The following table describes the relationships between the activities, their predecessors, and the estimated activity times (in weeks) for this project. (10 points)

1. Using this data, develop a network for this project.
2. Identify the critical path and determine the expected time of completion of the project.
3. Prepare the detailed activity schedule for this project (i.e., provide a table showing EST, EFT, LST, LFT, Slack, critical path?).
4. Determine the probability that the project will be completed in:

1. Less than 42 weeks
2. Greater than 35 weeks
3. Between 42 to 44 weeks
4. Greater than 40 weeks

What is the difference between a pdf and a cdf? How are they related?

Explain this as you would to someone who wasn't in class when I did. Assume they have taken Calculus 2. You can use text, pictures, a video, a dance, a song... whatever you want. Be creative! Submit your explanation as one file (a pdf for text or image, a single video or audio file etc.)

In which stages of the data investigation cycle would you consider (a) level of measurement and (b) choice of research design? Explain. (open-ended question)

An electronics store has 4 branches in a large city. They are curious if sales in any particular department are different depending on location. They take a random sample of purchases throughout the 4 branches – the results are recorded below. Run an independence test for the data below at the 0.05 level of significance.

What is the Test statistic (?2) and how is it done in excel?

Test the claim about the population mean,

muμ ,

at the given level of significance using the given sample statistics. Claim:

muμequals=4040 ;

alphaαequals=0.060.06 ;

sigmaσequals=3.873.87.

Sample statistics:

x overbarxequals=38.738.7 ,

nequals=7676

Identify the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0H0 :

muμequals=4040

Upper H Subscript aHa :

muμgreater than>4040

B.

Upper H 0H0 :

muμgreater than>4040

Upper H Subscript aHa :

muμequals=4040

C.

Upper H 0H0 :

muμequals=4040

Upper H Subscript aHa :

muμnot equals≠4040

D.

Upper H 0H0 :

muμequals=4040

Upper H Subscript aHa :

muμless than<4040

E.

Upper H 0H0 :

muμless than<4040

Upper H Subscript aHa :

muμequals=4040

F.

Upper H 0H0 :

muμnot equals≠4040

Upper H Subscript aHa :

muμequals=4040

Calculate the standardized test statistic.

The standardized test statistic is

nothing .

(Round to two decimal places as needed.)

Determine the critical value(s). Select the correct choice below and fill in the answer box to complete your choice.

(Round to two decimal places as needed.)

A.

The critical values are

plus or minus±nothing .

B.

The critical value is

nothing .

Determine the outcome and conclusion of the test. Choose the correct answer below.

A.

Fail to rejectFail to reject

Upper H 0H0.

At the

66 %

significance level, there

is notis not

enough evidence to reject the claim.

B.

Fail to rejectFail to reject

Upper H 0H0.

At the

66 %

significance level, there

is notis not

enough evidence to support the claim.

C.

RejectReject

Upper H 0H0.

At the

66 %

significance level, there

isis

enough evidence to reject the claim.

D.

RejectReject

Upper H 0H0.

At the

66 %

significance level, there

isis

enough evidence to support the claim.

Suppose a company surveyed the work preferences and attitudes of 1,006 working adults spread over three generations: baby boomers, Generation X, and millennials. In one question, individuals were asked if they would leave their current job to make more money at another job. The sample data are summarized in the following table.

Conduct a test of independence to determine whether interest in leaving a current job for more money is independent of employee generation.

State the null and alternative hypotheses.

H₀: Interest in leaving job for more money is not mutually exclusive of the employee generation.
H_a: Interest in leaving job for more money is mutually exclusive of the employee generation.

H₀: Interest in leaving job for more money is independent of the employee generation.
H_a: Interest in leaving job for more money is not independent of the employee generation.    

H₀: Interest in leaving job for more money is not independent of the employee generation.
H_a: Interest in leaving job for more money is independent of the employee generation.

H₀: Interest in leaving job for more money is mutually exclusive of the employee generation.
H_a: Interest in leaving job for more money is not mutually exclusive of the employee generation.

Find the value of the test statistic. (Round your answer to two decimal places.)

What is the p-value? (Round your answer to four decimal places.)

Using a 0.05 level of significance, what is your conclusion?

Do not reject H₀. We conclude that interest in leaving a job for more money is not independent of the employee generation.

Reject H₀. We conclude that interest in leaving a job for more money is not independent of the employee generation.     

Do not reject H₀. We cannot conclude that interest in leaving a job for more money is independent of the employee generation.

Reject H₀. We cannot conclude that interest in leaving a job for more money is independent of the employee generation.

1. Periodically, the county Water Department tests the drinking water of homeowners for contminants such as lead and copper. The lead and copper levels in water specimens collected in 1998 for a sample of 10 residents of a subdevelopement of the county are shown below.

(a)    Construct a 99% confidence interval for the mean lead level in water specimans of the subdevelopment.
≤μ≤

(b)    Construct a 99% confidence interval for the mean copper level in water specimans of the subdevelopment.  
≤μ≤

2.

The scientific productivity of major world cities was the subject of a recent study. The study determined the number of scientific papers published between 1994 and 1997 by researchers from each of the 20 world cities, and is shown below.

Construct a 97 % confidence interval for the average number of papers published in major world cities.

<μ<

List three variables, and how they are measured, for which you would use the mode as the most appropriate measure of central tendency.

Suppose you have a bag containing 2 red marbles, 3 white marbles, and 4 blue marbles.

a) if you draw 3 marbles simultaneously, what is the probability that you get one of each color?

b) If you draw 3 marbles one at a time, what Is the probability that you get one of each color?

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 100 minutes and a standard deviation of 20 minutes. Answer the following questions.

(a)What is the probability of completing the exam in one hour or less?

(b) What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes?

(c) Assume that the class has 90 students and that the examination period is 130 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time