Engineers concerned about a tower's stability have done extensive studies of its increasing tilt. Measurements of the lean of the tower over time provide much useful information. The following table gives measurements for the years 1975 to 1987. The variable "lean" represents the difference between where a point on the tower would be if the tower were straight and where it actually is. The data are coded as tenths of a millimeter in excess of 2.9 meters, so that the 1975 lean, which was 2.9642 meters, appears in the table as 642. Only the last two digits of the year were entered into the computer.

(a) Plot the data. Consider whether or not the trend in lean over time appears to be linear. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) What is the equation of the least-squares line? (Round your answers to three decimal places.)
y =  +  x

What percent of the variation in lean is explained by this line? (Round your answer to one decimal place.)
%

(c) Give a 99% confidence interval for the average rate of change (tenths of a millimeter per year) of the lean. (Round your answers to two decimal places.)
(  ,  )

Serum glutamic oxaloacetic transaminase (SGOT) is an enzyme that elevates when the heart muscle is damaged. Assume that the population distribution of SGOT levels in adults with healthy hearts is known to be normally distributed with ? = 18.5 units/L and ? = 13.2 units/L.

a. What proportion of adults with a healthy heart have an SGOT level of above 25 units/L? (0.5pts)

b. For a sample size of ? = 40 from this population, what would be the sampling distribution of the mean SGOT level? Include the type of distribution and the values of the defining parameters. (0.5pts)

c. Now suppose you collected a sample of ? = 40 adults who recently underwent heart surgery. If the sample mean SGOT level you got was above 25 units/L, do you think that the SGOT level of people who have recently undergone heart surgery actually has a distribution with ? = 18.5 units/L? Why or why not?

For each of the following scenarios, state the appropriate null hypothesis and indicate whether the result corresponds to a Type-I error, a Type-II error, or no error. Use α=0.05. (1pt each)

a. A new method of relaxation training, which includes mediation and biofeedback, is reported to be successful at reducing high blood pressure, even though it doesn’t actually have any effect on blood pressure.

b. A study that tested if there was any relationship between a person’s heart rate and consuming a small amount of caffeine resulted in a p-value of 0.21. In truth, there is no relationship between heart rate and caffeine in this population.

c. Park officials tested if new design of bear-proof trash bins is more successful at keeping bears out than the bins they currently use. Fact is that the new design is actually more successful than the current one. Their test resulted in a p-value of 0.08.

Suppose a coin is tossed 100 times and the number of heads are recorded. We want to test whether the coin is fair. Again, a coin is called fair if there is a fifty-fifty chance that the outcome is a head or a tail. We reject the null hypothesis if the number of heads is larger than 55 or smaller than 45.

Write your H_0 and H_A in terms of the probability of heads, say p.

Find the Type I error rate if the null hypothesis is true.

Calculate the power of the test if the true chance of head is 0.4

Find the p-value if the observed number of heads is 65.

•Example: A manager of a liquor store believes that the proportions of customers preferring CURES Beer, HAMMERKILL Beer, and MULER Beer are 40%, 30% and 30% respectively. The following results were obtained from a random sample of 200 customers:

•a) What type of data do we have here?

•b) Do the data provide sufficient evidence to indicate that the distribution of customer preferences is significantly different from the manager’s belief? Use a 1% level of significance.

Question 4 Researchers studied four different blends of gasoline to determine their effect on miles per gallon (MPG) of a car. An experiment was conducted with a total of 28 cars of the same type, model, and engine size, with 7 cars randomly assigned to each treatment group. The gasoline blends are referred to as A,B,C, and D.The MPGs are shown below in the table Gasoline Miles Per Blend Gallon A 26 28 29 23 24 25 26 B 27 29 31 32 25 24 28 C 29 31 32 34 24 28 27 D 30 31 37 38 36 35 29 We want to test the null hypothesis that the four treatment groups have the same mean MPG vs. the alternative hypothesis that not all of the means are equal. a) Before carrying out the analysis, check the validity of any assumptions necessary for the analysis you will be doing. Write a brief statement of your findings b) Test the null hypothesis that the four gasoline blends have the same mean MPGs, i.e., Test Ho: ua=ub=uc=ud vs. the alternative hypothesis Ha: not all the means are equal. c) If your hypothesis test in (b) indicates a significant difference among the treatment groups, conduct pairwise multiple comparison tests on the treatment group means. Underline groups of homogeneous means. d) Briefly state your conclusions. ( Use IBM SPSS for all calculations)

You are given the returns for the following three stocks:

Calculate the arithmetic return, geometric return, and standard deviation for each stock. Do you notice anything about the relationship between an asset’s arithmetic return, standard deviation, and geometric return? Do you think this relationship will always hold?

In Lesson Seven you've learned to convert raw scores to standard scores and used the empirical rule to determine probabilities associated with those standard scores.

Random Decimal Fraction Generator

Here are your random numbers:

0.1613
0.8590
0.7911

1. Use the random decimal fraction generator at Random.org, linked here, to generate a list of three fractions with four decimal places(LIST random decimal fraction generator  IS ON TOP). Assume those decimal fractions represent probability values associated with z-scores. Then use the standard normal table to look up the z-score that is closest to matching with that probability. List them below. (3 points)
   1. probability value (generated fraction) =
   2. associated z-score =
   3. probability value (generated fraction) =
   4. associated z-score =
   5. probability value (generated fraction) =
   6. associated z-score =
2. Use another random decimal fraction generator at Random.org, linked here, to generate a list of ten two-digit random numbers between 10 and 30. Calculate the z-score of the median of the data set. (3 points)
3. What does the z-score of the data set median just above tell you about the shape of the distribution? How do you know this? (3 points)
4. If you were to take repeated random samples of n = 5 from the data set just above, what would be the expected value of the mean of the sampling distribution of sample means? (3 points)
5. Considering the set of ten two-digit random numbers above as a population, calculate the standard error of the mean for the samples in question 4. (3 points)

My question is based on the chart above : In the comments section following Goal #1, based upon your analysis of the evidence, summarize the findings for Goal #1. My comments should include any suggestions for further research or dat gathering based on questions arising out of these data that I feel still need to be addressed.

The problem is I am not good with this at all. Any help would be greatly appreciated.

Expected number of time intervals until the Markov Chain below is in state 2 again after starting in state 2?

Matrix:

[.4,.2,.4]

[.6,0,.4]

[.2,.5,.3]

It is rare that you will find a gas station these days that only sells gas. It has become more common to find a convenient store that also sells gas. The data named “Convenient Shopping data” the sales over time at a franchise outlet of the major US oil company. Each row summarize sales for one day. This particular station sells gas and has a convenient store and car awash. The column labeled Sales gives the dollar sales of the convenient store and the column Volume gives the number of gallons of gas sold.

1) Draw a scatter plot for Sales on Volume where Sales is dependent on Volume of gas sold. Does there appear to be a linear pattern that relates to these two sequences?

2) Estimate the linear regression model using excel analysis tool I showed you in class. Write the linear model and interpret the slope (b1).

3) Interpret the R² and tell if your linear model is a good fit or not.

4) Estimate the difference in sales at the convenient store (on average) between a day with 3,500 gallons sold and a day with 4,000 gallons sold.

5) With regard to inference statistics, formulate a hypothesis test for the slope (b1) and decide if it is statistically significant or not.

6) Construct a 95% confidence interval for the slope.

The excel data are flash durations, in milliseconds, of a sample of 35 male fireflies of the species Photinus(Cratsley and Lewis 2003). You must use excel tools data analysis and descriptive statistics to find the confidence interval. Use the video as a guide to complete this excel project. If you do not see the data analysis, I have steps on how to get the data analysis tool on this document.

1. Estimate the sample mean flash duration. What does this quantity estimate?
2. Is the estimate in part(a) likely to equal the population parameter? Why or why not?
3. Paste the descriptive statistics output from excel
4. Use the descriptive statistics output to record the standard error for your estimate.
5. What does the quantity in part(d) measure?
6. Use excel output to calculate the 95% confidence interval for the population mean.
7. Provide an interpretation for the interval you calculated in part(f)

PLEASE SHOW ALL WORK WHEN POSSIBLE!

Data:

A school psychologist wishes to determine whether a new anti-smoking film actually reduces the daily consumption of cigarettes by teenage smokers. The mean daily cigarette consumption is calculated for each of eight teenage smokers during the month before and the month after the film presentation, with the following results: MEAN DAILY CIGARETTE CONSUMPTION

SMOKER NUMBER BEFORE FILM (X1) AFTER FILM (X2)

1 28 26

2 29 27

3 31 32

4 44    44

5 35 35

6 20 16

7 50 47

8 25 23

A) Is there a significant difference in the number of cigarettes smoked before the film as compared to the number of cigarettes smoked after the film?

B) What does this NOT necessarily mean?

C) What might be done to improve the design of this experiment?

COMPUTER CALCULATIONS:

I need to know how to code in R for the solutions, not by hand.

2. Look at the data in Table 7.18 on page 368 of the textbook. These data are also

given in the SAS code labeled “SAS_basketball_goal_data” and R code labeled basketball goal data .

The dependent variable is goals and the independent variable is height of basketball players.

Complete a SAS /R program and answer the following questions about the data set:

(a) Does a scatter plot indicate a linear relationship between the two variables?

Is there anything disconcerting about the scatter plot? Explain.

(b) Fit the least-squares regression line (using SAS / R) and interpret the estimated slope

in the context of this data set. Does it make sense to interpret the estimated intercept? Explain.

(c) For these data, what is the unbiased estimate of the error variance? (Give a number.)

(d) Using the SAS / R output, test the hypothesis that the true slope of the regression line

is zero (as opposed to nonzero). State the appropriate null and alternative hypotheses,

give the value of the test statistic and give the appropriate P-value. (Use significance

level of 0.05.) Explain what this means in terms of the relationship between the two

variables.

(e) Using SAS / R, find a 95% confidence interval for the mean basketball goal for

a player with a height of 77 inches. In addition find a 95% prediction interval for

basketball goal for a player with a height of 77 inches.

Data:

A sample of 1000 customers was selected in Rhode Island to determine various information concerning consumer behavior. Among the questions asked was “Do you enjoy shopping at Shopping Center A?” The results are summarized in the following table.

1. Is there evidence of a significant difference between males and females in the proportion who enjoy shopping at Shopping Center A at the 0.01 level of significance?
2. Construct and interpret a 95% confidence interval estimate for the difference between the proportion of males and females who enjoy shopping at Shopping Center A.