The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends on many factors, including the model year, mileage, and condition. To investigate the relationship between the car’s mileage and the sales price for Camrys, the following data show the mileage and sale price for 19 sales (PriceHub web site, February 24, 2012).

DATA

Miles (1,000s) Price ($1,000s) 22 16.2 29 16.0 36 13.8 47 11.5 63 12.5 77 12.9 73 11.2 87 13.0 92 11.8 101 10.8 110 8.3 28 12.5 59 11.1 68 15.0 68 12.2 91 13.0 42 15.6 65 12.7 110 8.3

(a) Choose a scatter chart below with ‘Miles (1000s)’ as the independent variable. (i) (ii) (iii) (iv) What does the scatter chart indicate about the relationship between price and miles? The scatter chart indicates there may be a linear relationship between miles and price. Since a Camry with higher miles will generally sell for a lower price, a negative relationship is expected between these two variables. This scatter chart is consistent with what is expected.

(b) Develop an estimated regression equation showing how price is related to miles. What is the estimated regression model? Let x represent the miles. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) = + x

(c) Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.01 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(d) How much of the variation in the sample values of price does the model estimated in part (b) explain? If required, round your answer to two decimal places. %

(e) For the model estimated in part (b), calculate the predicted price and residual for each automobile in the data. Identify the two automobiles that were the biggest bargains. If required, round your answer to the nearest whole number. The best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price. The second best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price.

(f) Suppose that you are considering purchasing a previously owned Camry that has been driven 100,000 miles. Use the estimated regression equation developed in part (b) to predict the price for this car. If required, round your answer to one decimal place. Do not round intermediate calculations. Predicted price: $ Is this the price you would offer the seller?

Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Suppose that miles driven anually by cars in America are normally distributed with mean = 12; 894 miles and standard deviation = 1190 miles.

(a)If one car is chosen at random, what is the probability it has driven more than

13,000 miles last year?

(b) If a sample of 25 cars is taken, what is the probability that the mean of the

sample is less than 13,000 miles?

***A parameter is a value for a population, and a statistic

is a value for a sample.

T F

The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level).The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level).

1. Using “stories” as the independent variable and “height” as the dependent variable, make a scatter plot of the data.
2. Does it appear from inspection that there is a relationship between the variables?
3. Calculate the least squares line. Put the equation in the form of: ŷ = a + bx
4. Find the correlation coefficient. Is it significant?
5. Find the estimated heights for 32 stories and for 94 stories.
6. Based on the data in Table 12.24, is there a linear relationship between the number of stories in tall buildings and the height of the buildings?
7. Are there any outliers in the data? If so, which point(s)?
8. What is the estimated height of a building with six stories? Does the least squares line give an accurate estimate of height? Explain why or why not.
9. Based on the least squares line, adding an extra story is predicted to add about how many feet to a building?
10. What is the slope of the least squares (best-fit) line? Interpret the slope.

The Wheat producers of North America are expecting to match their supply to meet the change in the market demand during coming year that is expected to change. The current year market supply and supply function is assumed to be:

Q_D= 62.5 - 0.125P

Q_S= 0.5P - 100

Please predict either a rise or fall in the demand of wheat as a percentage change from the current year demand based on your observations from the website and derive a new demand function with the predicted percentage change (EITHER INCREASE OR DECREASE) in demand, (i.e. the quantity demanded will increase or decrease by THE PERCENTAGE for each level of price). (Please restrict your change in demand within ± 25%)

Please compute the following:

1. Market Equilibrium Price for current year and next year with percentage change.
2. Market Equilibrium Quantity for current year and next year with percentage change
3. Producer Surplus and Consumer Surplus for current year and following year with percentage change

The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level).

Calculate the least squares line. Put the equation in the form of:

ŷ = a + bx

Find the correlation coefficient r.

Find the estimated height for 34 stories. (Use your equation from part (c). Round your answer to one decimal place.)
ft

Find the estimated height for 93 stories

What is the estimated height of a building with 7 stories

Based on the least squares line, adding an extra story adds about how many feet to a building?

What is the slope of the least squares (best-fit) line?

The average "psychological health" score for college professors in America is µ = 24.00 on a standardized "psychological health" survey. A statistics student from Valpo wants to know if professors from Valpo have "psychological health" scores that are significantly different than the national average. The student has N = 36 Valpo professors complete the survey and finds that their M = 21.00 with a standard deviation of SD = 5.00. Test this prediction using a two-tailed test using an α = .05. What is the critical t value for this study?

A.±2.7238

B.±1.6896

C.±2.0301

D.±2.4377

The Grocery Manufactures of America reported that 76% of consumers read the ingredients listed on a product's label. Assume the a sample of 400 consumers is selected from the population.

a. Calculate the standard error of the proportion.

b. What is the probability that the sample proportion will be more than 81% of the population proportion?

c. What is the probability that the sample proportion will be within ± .03 of the population proportion?

d. Answer part (c) for a sample of 750 consumers.

1. A. An union representing the Bottle Blowers of America (BBA) is considering a proposal to merge with the Teamsters Union. According to BBA bylaws, at least three-fourths of the union membership must approve any merger. A random sample of 2,000 current BBA members reveals 1,600 plan to vote for the merger proposal. Develop a 95% confidence interval for the population proportion. Show point estimate, standard error and margin of error and finally your confidence interval.

Basing your decision on this sample proportion, can you conclude that the necessary         proportion of BBA members favor the merger? Why?                                                       

      B. The estimate of the population proportion is to be within plus or minus 0.10, with a 99% confidence coefficient level. The best estimate of the population proportion is given as 45%. How large a sample is required under these specifications?                                          

The Grocery Manufacturers of America reported that 65% of consumers read the ingredients listed on a product's label. Assume the population proportion is p=0.65 and a sample of 500 consumers is selected from the population.

(a) Show the sampling distribution of the sample proportion (p-bar) where, (p-bar) is the proportion of the sampled consumers who read the ingredients listed on a product's label. (1) E(p)= (xxxx) (2 decimals) (2) std dev of (p-bar) = (xxxx)

(b) What is the probability that the sample proportion will be within .03 of the population proportion (to 4 decimals).

(c) . Answer part (b) for a sample of 600 (to 4 decimals).

According to the Anxiety and Depression Association of America, over 20% of Americans are diagnosed with anxiety and/or depression (2018). As we learn about the nervous system this module, we can use these two common disorders to help gain an understanding of basic nerve function.

For your discussion post, choose either depression or anxiety and answer the following questions. Remember to use your own words when explaining these concepts.

• How does depression/anxiety affect neurotransmitters?
• How does depression/anxiety affect synapses?
• How does depression/anxiety affect neuron function?

In your reply posts, share how various treatments may improve the physiology of the disorders discussed. Since these are common disorders, you may choose to share personal experiences. If so, keep the information you share confidential and do not share names or identifying information of others.