The mean pay in 2008 Bh CEOsat the 500 biggest U.S. companies was 12.8 million dollars.”” Public outcry and stockholder complaints have forced compensation committees to reconsider senior executive salaries. A random sample of CEOs was obtained, and the total pay (in millions of dollars) for each is given in the following table.

10.1 4.3 13.8 5.1 13.0 21.2 4.5 10.5 17.6 10.1 6.5 9.9 13.3 20.4

Is there any evidence to suggest that the mean pay for CEOs has decreased? Use a = 0.05 and assume normality.

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STAT 213 Assignment 3: Problem 5

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To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?

Expected value =

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Equation Editor

A previous analysis of historical records found that the mean value of orders for promotional goods is 35 dollars, with the company earning a gross profit of 22% on each order. Calculate the expected value of the profit contribution next year.

Expected value =

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Equation Editor

The fixed cost of conducting the four promotions is estimated to be 17000 dollars with a variable cost of 2 dollars per customer for mailing and handling costs. What is the minimum number of customers required by the company in order to cover the cost of promotions? (Round your answer to the next highest integer.)

Breakeven point =

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Equation Editor

1. The table below contains price-demand and total cost data for the production of projectors, where p is the wholesale price (in dollars) of a projector for an annual demand of x projectors and C is the total cost (in dollars) of producing x projectors.

Price-Demand:

a. Make a scatter plot for p vs x (price-demand plot).

b. Get a regression line that best fits the data in Question a. You need to type the equation of this line in desmos and graph it with your scatter plot. Please use p(?1) = equation when typing in desmos.

c. Does it look like the regression line models the data well? (Yes or No) Why?

d. Use the equation typed in desmos to find p(0), p(3000), p(6000) 5. What value of x would make p(x) = 0?

1.Crop rotation is a common strategy used to improve the yields of certain crops in subsequent growing seasons. An experiment was performed to assess the effects of crop rotation plant type and crop rotation plant density levels on the yield of corn, the primary crop of interest. A field was separated into 12 plots and each of the treatments was randomly applied. After 2 months of growth of the rotated crops, the plots were cleared, and corn seeds were applied evenly to each plot. After 5 months of growth of the corn, the yields were assessed. The data, in kg/m2, are shown below. Determine if crop rotation plant type and density affect the yields of corn in this field. What treatment should the farmers use to maximize the yield?

1. What kind of statistical test will you be performing?
2. Will you need to test for equal variance? If so what are your results and how does that influence the next steps in your analysis?
3. What are your null and alternative hypotheses?
4. Discuss the results of your analysis. Will you accept or reject your null hypothesis? Why? What can you specifically say about the data?

For each of the different confidence levels given below determine the appropriate z* to use to create a confidence interval for the population proportion. (Give the positive z* value, rather than the negative.)

C= 88%, z*=

C= 93%, z*=

C= 72%, z*=

The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The population mean is thought to be 100, and the population standard deviation σ is 2. You wish to test H0 : µ = 100 versus H1 : µ 6= 100. Note that this is a two-sided test and they give you σ, the population standard deviation. (a) State the distribution of X¯ assuming that the null is true and n = 9.

(b) Find the boundary of the rejection region for the test statistic (these critical values will be z-values) if the type I error probability is α = 0.01.

(c) Find the boundary of the rejection region in terms of ¯x if the type I error probability is α = 0.01. In other words, how much lower than 100 must X¯ be to reject and how much higher than 100 must X¯ be to reject. You will have an ¯xlow and an ¯xhigh defining the rejection region. HINT: You are un-standardizing your z from part (b) here.

(d) What is the type I error probability α for the test if the acceptance region for the hypothesis test is instead defined as 98.5 ≤ x¯ ≤ 101.5? Recall that α is the probability of rejecting H0 when H0 is actually true.

​​​​​​The following table shows age distribution and location of a random sample of 166 buffalo in a national park.

Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Age distribution and location are not independent.
H₁: Age distribution and location are not independent.H₀: Age distribution and location are independent.
H₁: Age distribution and location are independent.    H₀: Age distribution and location are not independent.
H₁: Age distribution and location are independent.H₀: Age distribution and location are independent.
H₁: Age distribution and location are not independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

uniformchi-square    normalStudent's tbinomial

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.1000.050 < p-value < 0.100    0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that age distribution and location are not independent.At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.    

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 5 percentage points with 95​% confidence if ​(a) he uses a previous estimate of 22​%? ​(b) he does not use any prior​ estimates? Round up the answer to the nearest integer

Suppose in July of 2008, the true proportion of U.S. adults that thought unemployment would increase was 47%. In November of 2008, the same question was asked to a simple random sample of 1000 U.S. adults and 432 of them thought unemployment would increase. Can we conclude that the true proportion of U.S. adults that thought unemployment would increase in November is less than the proportion in July? Use a 5% significance to test.
Round to the fourth
H0: Select an answer x̄ p̂ μ p  Select an answer = < > ≠  
HA: Select an answer x̄ p̂ μ p  Select an answer = < > ≠  
What's the minimum population size required?
How many successes were there?
Test Statistic:
P-value:
Did something significant happen? Select an answer Significance Happened Nothing Significant Happened
Select the Decision Rule: Select an answer Reject the Null Accept the Null Fail to Reject the Null
Select an answer: is or is not  enough evidence to conclude Select an answer that the true proportion of U.S. adults that thought unemployment would increase in November is less than 0.47 that the true proportion of U.S. adults that thought unemployment would increase in November is more than 0.47 that the true proportion of U.S. adults that thought unemployment would increase in November is 0.47

Build a 90% confidence interval and decide if you can conclude the same. Use your calculator to do this and round to the fourth decimal place.
( , )
Can we conclude the same as our Hypothesis Test?
Select an answer no yes  because the true proportion of U.S. adults in November 2008 that thought unemployment would increase

A electronics manufacturer has developed a new type of remote control button that is designed to operate longer before failing to work consistently. A random sample of 28 of the new buttons is selected and each is tested in continuous operation until it fails to work consistently. The resulting lifetimes are found to have a sample mean of ?¯x¯ = 1254.6 hours and a sample standard deviation of s = 109.1. Independent tests reveal that the mean lifetime of the best remote control button on the market is 1225 hours. Conduct a hypothesis test to determine if the new button's mean lifetime exceeds 1225 hours. Round all calculated answers to four decimal places.

2. Which of the following conditions must be met to perform this hypothesis test? Select all the correct answers.

A. The sample must be large enough so that at least 10 buttons fail and 10 succeed.
B. The observations must be independent.
C. We must be able to expect that at least 5 buttons will fail to work consistently.
D. The number of remote control buttons tested must be normally distributed.
E. The lifetime of remote control buttons must be normally distributed.

3. Calculate the test statistic  ? z t X^2 F  =

4. Calculate the p-value

5. Calculate the effect size, Cohen's d, for this test. ?̂ d^ =

6. The results of this test indicate we have a...
A. small
B. large
C. moderate to large
D. small to moderate
effect size, and...
A. extremely strong evidence
B. some evidence
C. strong evidence
D. very strong evidence
E. little evidence
that the null model is not compatible with our observed result.

Randomly selected 10 student cars have ages with a mean of 7.2 years and a standard deviation of 3.4 years, while randomly selected 31 faculty cars have ages with a mean of 5.9 years and a standard deviation of 3.5 years.

1. Use a 0.01 significance level to test the claim that student cars are older than faculty cars.

(a) The test statistic is

(b) The critical value is 2.326

(c) Is there sufficient evidence to support the claim that student cars are older than faculty cars? A. No B. Yes

2. Construct a 99% confidence interval estimate of the difference μs−μf, where μs is the mean age of student cars and μf is the mean age of faculty cars. <(μs−μf)<

The x2 statistic from my study was close to zero, so I rejected the null hypothesis.

The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $105. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $560 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $250 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $470 (to 4 decimals)?

d. What is the cost for the 2% highest domestic airfares? (rounded to nearest dollar) $ or Select your answer 1. More 2. Less

A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Listed below are the amounts of mercury​ (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 90​% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna​ sushi? 0.54  0.82  0.09  0.96  1.28  0.54  0.96

What is the confidence interval estimate of the population mean?

Use this information to draw an appropriate conclusion about whether there could be too much mercury in tuna sushi

What social media tools do marketers commonly use? A survey by Social Media Examiner of B2B marketers, marketers that primarily target businesses, and B2C marketers, marketers that primarily target consumers, reported that 344 (88%) of B2B marketers and 373 (61%) of B2C marketers commonly use LinkedIn as a social media tool. The study also revealed that 239 (61%) of B2B marketers and 324 (53%) of B2C marketers commonly use Google ++ plus as a social media tool. (Data extracted from 2014 Social Media Marketing Industry Report, bit.ly/1e896pD .)

Suppose the survey was based on 390 B2B marketers and 610 B2C marketers.

• a. At the 0.05 level of significance, is there evidence of a difference between B2B marketers and B2C marketers in the proportion that commonly use LinkedIn as a social media tool?

• b. Find the p-value in (a) and interpret its value.

• c. At the 0.05 level of significance, is there evidence of a difference between B2B marketers and B2C marketers in the proportion that commonly use Google ++ plus as a social media tool?

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