You are at a wetland site. You have been instructed to test for chromium contamination. Suppose that a regulatory agency has determined that a population mean chromium concentration equal to 7 mg/kg characterizes the no-contamination state. Likewise, a population mean chromium concentration significantly greater than 7 mg/kg characterizes the contamination state. Suppose that 12 soil tests were conducted around different areas around the wetland site. Their chromium concentration analyzed with the following results. Use this information for the 9 problems. Do not round.

6.223 6.995 10.333 7.265 7.833 7.111 6.986 8.934 9.167 7.505 7.301 7.213

1. Describe the population of interest and hypothesized parameter for this scenario.

2. Find the mean of the sample. Use the formula and show the steps for finding the sample mean.

3. Find the median of the sample. Use the formula and show the steps for finding the sample median.

4. Find the standard deviation of the sample. Use the formula and show the steps.

5. Using the appropriate symbols, write the hypotheses.

6. Calculate the test statistic showing the work with the formula.

7. Using StatCrunch, determine the p-value for the hypothesis test using the appropriate probability distribution (do not just use the t test for a single mean output).

8. Make the decision for the test in terms of the null hypothesis. Explain how you arrive at this decision.

9. Write the conclusion with minimal statistical jargon and answer the research question of interest as demonstrated in the presentations.

We work for Cola Company and there have been some discussions on which pressure setting is best for filling out bottles. If we overfill the bottles then we are spending money we do not need to. If we are under filling the bottles we run the risk of dissatisfaction of the customers. If we can fill the bottles using a higher psi we can run the line faster and thus increase our production. Our current fill pressure is 25psi. Management wants to know if there is a different variation from the standard between the two pressure settings.

ml (25psi volume): 1007.2, 1008.4, 1010.2, 1011.2, 1008.0, 1009.0, 1011.4, 1013.4, 1010.6, 1010.9

ml (30psi volume): 1001.2, 1003.1, 1003.6, 1001.4, 1002.7, 1004.3, 1002.6, 1005.0, 1003.7, 1004.4

Sample size of first set =

Sample size of second set =

Sample mean of first set =

Sample mean of second set =

Sample standard deviation of the first set =

Sample standard deviation of the second set =

Estimate of variance =

Confidence Coefficient =

Alpha =

Calculated Degrees of Freedom =

Calculated Test Statistic =

What can you conclude by observing your confidence limits? (No difference or there is a difference?) =

Consider the following data: 43 54 55 63 67 68 69 77 85 Suppose that the last value is actually 115 instead of 85. What effect would this new maximum have on the median of the data?

increase the value of the median

decrease the value of the median

no effect

1. Approximately, what z-score divides the lower 75% of the data from the upper 25%?

   1. z = 0.75

   2.   z = 0.675

   3.   z = - 0.675

   4.   z = -0.25

   5.   none of the above

Shown below is a portion of a computer output for a regression analysis relating Y (demand) and X (unit price). ANOVA df SS Regression 1 Error 3132.661 Total 47 8181.479 Coefficients Standard Error Intercept 80.390 3.102 X -2.137 0.248 (a) Compute the coefficient of determination and fully interpret its meaning. Be very specific. (b) Find the standard error for b1 (Sb1). (c) Perform a t test and determine whether or not demand and unit price are related. Let  = 0.05. (d) Perform an F test and determine whether or not demand and unit price are related. Let  = 0.05

1. Differentiate

• Standard error of regression (Sy)

• Standard error of slope (Sm)

• Standard error of y-intercept (Sb)

1. At CES 2019, L’Oreal won the award for best innovation in wearable technology for their product, My Skin Track pH. The scientific and medical communities have long known the link between skin pH and common skin concerns, yet there has never been a consumer-friendly way to measure it. My Skin Track pH is the first-ever, wearable sensor and companion app to measure personal skin pH levels and create customized product regimens to better care for skin. Using microfluidics technology, the sensor captures trace amounts of sweat to provide an accurate skin pH reading. Conventional methods for reading pH levels include swabbing the skin for sweat and using a bulky digital pH meter. Researchers know that both methods provide accurate data,but were not sure which would provide results faster. A sample of seven subjects were brought in and each tested both methods. The data is shown below.

Using a significance level of 0.05, does one method provide results that are significantly faster?

Note that there are no correct answers per sec.

Each student is asked to respond based on his or her subjective evaluation. No calculations are required.

Each problem has individual, team, and class components.

Problem 1: Preferences You are given a choice between being awarded $1000 this time next year (with complete certainty), or a reduced amount of dollars today. How much would you be willing to settle for, in order to receive the award today?

Problem 2 Hypertension and the standard gamble Assume you suffer from severe hypertension that has led to blurry vision. If you continue to be treated with standard hypertension medications, you can expect to live another 25 years, but your vision problems will persist and become permanent. However, a new drug has come to the market, which can restore your vision to a nearly normal, with the same life expectancy of 25 years. However, the drug carries one critical side effect –it leads to immediate death. Taking the new drug is your personal choice. Would you agree to take this drug (which will cure your vision with certainty) if the chance of immediate death is given by one of the following probabilities:

A. 10% --- B. 25% --- C. 50% --- D. 75% --- E. 90%. ---

Please answer part a) through part d) of the question below. Thank you.

Question 3

A tobacco refinery has four methods of measuring pH. To test the
four methods, a supervisor randomly assigns each of 32 tobacco
samples with known pH to one of the four methods, so that each
method is applied to exactly eight samples. The difference between
measured pH and the known pH is recorded, and the data is below.

a) Use R to calculate the means and standard deviations for the four
methods. Based only on these numbers, do the mean pH differences
seem to differ across the methods? Explain.

b) Do the ANOVA conditions hold? Be sure to include your R code,
output, appropriate graphs (boxplots, dotplots), and explanations.

c) Regardless of your answer to (b), run ANOVA with R. Set-up your
null and alternative hypotheses; provide your test statistic, p-value,
and conclusion.

d) Use the Bonferroni adjustment to make a confidence interval for
each of the 6 differences between treatment means, using an
experiment-wise confidence level of 95%.

A store surveys customers to see if they are satisfied with the service they receive. Samples of 75 surveys are taken. One in six people are unsatisfied. What is the variance of the mean of the sampling distribution of sample proportions for the number of unsatisfied customers? What is the variance for satisfied customers?

The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of The Thomas Supply Company Inc. invoices.

13 13 13 20 26 30 31 32 34 34 35 35 36 37 38 41 41 41 45 46 47 47 48 52 54 56 56 62 67 82

(Round your answers to 2 decimal places.) a. Determine the first and third quartiles. Q1 Q3 b. Determine the second decile and the eighth decile. D2 D8 c. Determine the 67th percentile.

According to a​ survey, people in a certain country ate an average of 212 meals in restaurants in 2001. The data in the accompanying table show the number of meals eaten in restaurants as determined from a random sample of people in this country in 2009. Using alpha equals =0.02. Test the hypothesis that the number of meals eaten at restaurants by people in this country has not changed since 2001.

Determine the test​ statistic....???

Data Table:

202 134 199 361 147 80 176 308 58 208

168 330 89 216 270 289 228 337 203 169

.

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 39 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.88 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error?

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.29 for the mean price per 100 pounds of watermelon.

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds.

What is the expectation for the number of face cards (aces not included) when 10 cards are drawn, with replacement, from a standard deck

Assume that the time needed to complete a midterm exam for a particular course is normally distributed with a mean of 90 minutes and a standard deviation of 15 minutes.

5- What percentage of the class is expected to complete the exam within 60 minutes?

6- What percentage of the class is predicted to NOT complete the exam within 115 minutes?

7- If the time limit is 100 minutes and there are 200 students in the class, how many of them do you predict to not complete the exam within the allocated time?

Each​ year, ratings are compiled concerning the performance of new cars during the first 60 days of use. Suppose that the cars have been categorized according to whether a car needs​ warranty-related repair​ (yes or​ no) and the country in which the company manufacturing a car is based​ (in some country X or not in country​ X). Based on the data​ collected, the probability that the new car needs a warranty repair is 0.07​, the probability that the car is manufactured by a company based in country X is 0.50, and the probability that the new car needs a warranty repair and was manufactured by a company based in country X is 0.025. Use this information to answer​ (a) through​ (d) below.

a.Suppose you know that a company based in country X manufactured a particular car. What is the probability that the car needs warranty​ repair?

​(Round to three decimal places as​ needed.)

b. Suppose you know that a company based in country X did not manufacture a particular car. What is the probability that the car needs warranty​ repair?

​(Round to three decimal places as​ needed.)

c. Are need for warranty repair and location of the company manufacturing the car​ independent?

A.

No

B.

Yes

C.

Not enough information