Suppose the data shown here are the results of a survey to investigate gas prices. Ten service stations were randomly selected in each city and the figures represent the prices of a litre of unleaded regular gas. What can we tell about the relative price of gas in the two cities?

City 1:

City 2:

Design a test to determine if there is a difference in mean gas prices in the two cities use alpha = .01

What does Probability have to do with the real world? Give specific examples how it relates in a couple of paragraphs.

Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted and fuel wasted. Let x represent the average annual hours per person spent in traffic delays and let y represent the average annual gallons of fuel wasted per person in traffic delays. A random sample of eight cities showed the following data. x (hr) 29 5 23 37 18 23 19 5 y (gal) 45 3 31 53 31 38 28 9 (a) Draw a scatter diagram for the data. Submission Data Correct: Your answer is correct. Verify that Σx = 159, Σx2 = 4003, Σy = 238, Σy2 = 9074, and Σxy = 6003. Compute r. The data in part (a) represent average annual hours lost per person and average annual gallons of fuel wasted per person in traffic delays. Suppose that instead of using average data for different cities, you selected one person at random from each city and measured the annual number of hours lost x for that person and the annual gallons of fuel wasted y for the same person. x (hr) 22 4 19 40 19 26 2 39 y (gal) 63 8 12 54 21 35 4 71 (b) Compute x and y for both sets of data pairs and compare the averages. x y Data 1 Data 2 Compute the sample standard deviations sx and sy for both sets of data pairs and compare the standard deviations. sx sy Data 1 Data 2 In which set are the standard deviations for x and y larger? The standard deviations for x and y are larger for the first set of data. The standard deviations for x and y are larger for the second set of data. The standard deviations for x and y are the same for both sets of data. Correct: Your answer is correct. Look at the defining formula for r. Why do smaller standard deviations sx and sy tend to increase the value of r? Dividing by smaller numbers results in a smaller value. Multiplying by smaller numbers results in a larger value. Multiplying by smaller numbers results in a smaller value. Dividing by smaller numbers results in a larger value. Correct: Your answer is correct. (c) Make a scatter diagram for the second set of data pairs. Submission Data Correct: Your answer is correct. Verify that Σx = 171, Σx2 = 5023, Σy = 268, Σy2 = 13,816, and Σxy = 7892. Compute r. (d) Compare r from part (a) with r from part (b). Do the data for averages have a higher correlation coefficient than the data for individual measurements? No, the data for averages do not have a higher correlation coefficient than the data for individual measurements. Yes, the data for averages have a higher correlation coefficient than the data for individual measurements. Correct: Your answer is correct. List some reasons why you think hours lost per individual and fuel wasted per individual might vary more than the same quantities averaged over all the people in a city.

1. Given the following table of possible values for rv Z and the number of possible ways that this value can occur,
   1. Construct the pmf and cdf for this rv
   2. Graph the cdf
   3. Calculate Pr(Z=6)
   4. Calculate Pr(Z=2)
   5. Calculate Pr(Z > 4 or Z ≤ 2)
   6. Calculate Pr( 1 < Z ≤ 6)
   7. Calculate Pr( Z ≤ 3 | Z < 9 )

Small-company stocks funds are prone to periodic bursts of hot performance. Consider the five small-company mutual funds and their performance, as listed below. Small-Company Performance over the Performance over the Mutual Fund Past 12 Months Past 5 Years Babson Enterprises II 31.8% 119% Eclipse Equity 33.8% 131% Fasciano 25.3% 133% Gabelli Small Cap Growth 36.8% 123% Nicholas Limited Edition 30.0% 119% Construct a bar chart for the 12-month performance and another bar chart for the 5-year performance.

A ["prospective", OR "retrospective"] cohort study is carried out to investigate the association between occupational arsenic inhalation and neurological exposure and neurological effects among workers in a copper smelter. For the sake of simplicity, let’s assume there are two possible exposure categories: high and low (for example, those working in the smelting process and those working in administration). The exposure was carefully assessed by review of company records which reflected very good exposure monitoring (both air sampling and urine testing). The outcome was based on self-reported information from an interview that asked: “Have you had tingling in your fingers in the last month that lasted more than 30 minutes?” Those that said “yes” were classified as “diseased”, and those that said “no” were the “non-diseased” group. In order to avoid ["information bias", OR "selection bias"]   bias, the company encouraged everyone to participate by telling their workers that they were a concerned employer and wanted to know if there were adverse neurological effects from the potential arsenic exposure in some of the work areas.

The following is the resulting 2 x 2 table:

The probability that a certain hockey team will win any given game is 0.3628 based on their 13 year win history of 377 wins out of 1039 games played (as of a certain date). Their schedule for November contains 12 games. Let X = number of games won in November. Find the probability that the hockey team wins at least 7 games in November. (Round your answer to four decimal places.)

Please use TI-84 calculator not excel. Thanks!

A study was conducted to determine if the number of hours spent studying for an exam is associated with the exam score. The following are the observations obtained from a random sample of 5 students:

The average number of hours spent studying for an exam is _____.

Part A:

The average exam score is _____.

Part B:

The sum of squared differences of the number of hours spent studying from its mean (SSx) is _____.

Part C:

The sum of squared differences of the exam score from its mean (SSy) is _____.

Part D:

The standard deviation of the number of hours spent studying is _____.

Part E:

The standard deviation of exam scores is _____.

Part F:

Consider the following random sample observations on stabilized viscosity of asphalt specimens.

Suppose that for a particular application, it is required that true average viscosity be 2000. Is there evidence this requirement is not satisfied? From previous findings we know that the population standard deviation, σ = 89.3.
State the appropriate hypotheses. (Use α = 0.05.)

H₀: μ ≠ 2000

H_a: μ = 2000

H₀: μ > 2000

H_a: μ < 2000

H₀: μ = 2000

H_a: μ ≠ 2000

H₀: μ < 2000

H_a: μ = 2000

Calculate the sample mean and standard error. (Round your answers to three decimal places.)

Test the appropriate hypotheses. (Round your z test statistic to two decimal places and your p-value to four decimal places.)

What can you conclude?

Do not reject the null hypothesis. There is strong evidence to conclude that the true average viscosity differs from 2000.

Reject the null hypothesis. There is strong evidence to conclude that the true average viscosity differs from 2000.   

Reject the null hypothesis. There is no evidence to conclude that the true average viscosity differs from 2000.

Do not reject the null hypothesis. There is no evidence to conclude that the true average viscosity differs from 2000.

For right sided test for proportion, use z-table to find the critical value when alpha = .08

Please explain how to find

Twelve samples, each containing five parts, were taken from a process that produces steel rods. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were: Sample Sample Mean (in.) Range (in.) 1 10.002 0.011 2 10.002 0.014 3 9.991 0.007 4 10.006 0.022 5 9.997 0.013 6 9.999 0.012 7 10.001 0.008 8 10.005 0.013 9 9.995 0.004 10 10.001 0.011 11 10.001 0.014 12 10.006 0.009 a) Determine the upper and lower control limits and the overall means for -charts and R-charts. the answer states an equation using numbers i know how to get except .577 how did you get the .577

A group of researchers wants to estimate the true mean skidding distance along a new road in a certain forest. The skidding distances​ (in meters) were measured at 20 randomly selected road sites. These values are given in the accompanying table. Complete parts a through d.

a. Estimate the true mean skidding distance for the road with a 99% confidence interval.

(_____,_______)​(Round to one decimal place as​ needed.)

b. Give a practical interpretation of the​ interval, part a.

The confidence interval means that we are ______% confident that the true

Suppose the time between buses at a particular stop is a positively skewed random variable with an average of 60 minutes and standard deviation of 6 minutes. Suppose the time between buses at this stop is measured for a randomly selected week, resulting in a random sample of n = 36 times. The average of this sample,

X, is a random variable that comes from a specific probability distribution.

(a)Which of the following is true about the distribution of mean times for n = 36?

The distribution will be normally distributed with a mean of 60 minutes and a standard deviation of 6 minutes.

The distribution will be positively skewed with a mean of 60 minutes and a standard deviation of 6 minutes.   

The distribution will be normally distributed with a mean of 60 minutes and a standard deviation of 1 minutes.

The distribution will be positively skewed with a mean of 60 minutes and a standard deviation of 1 minutes.

(b) Calculate the probability the mean time for the sample of 36 buses will be between 59 minutes and 61 minutes.

P(59 ≤ X ≤ 61)

=  

(c) How likely is it the average time will exceeds 61 minutes?

P(X ≥ 61)

=

You may need to use the z table to complete this problem.

2-1- Based on Initial Observation values, calculate the mean and standard deviation of the data. (You need to show your calculation for standard deviation calculation). Then calculate the Cp and Cpk of the process based on provided USL and LSL in the article.

USL=105 mm

LSL=75 mm