The times (in seconds) for a sample of New York Marathon runners were as follows:

Conduct a two-way analysis of variance including interactions to examine these data. Perform model criticism. What do you conclude? Note that R users do not need to invoke the “car” package since the equal replication means that Type I = Type III SS (using car package can be tricky when fitting models with interactions since the contrasts also need to be altered to make them comparable).

You may need to use the appropriate appendix table or technology to answer this question.

A simple random sample of 400 individuals provides 128 Yes responses.

(a)

What is the point estimate of the proportion of the population that would provide Yes responses?

(b)

What is your estimate of the standard error of the proportion,

σ_p?

(Round your answer to four decimal places.)

(c)

Compute the 95% confidence interval for the population proportion. (Round your answers to four decimal places.)

to

1. What are the three major differences between a normal distribution and a binomial distribution?
2. Why is the Normal Distribution called "Normal"?
3. What are examples of exponentially distributed random variables in real life?
4. What is the significance of central limit theorem?

Anystate Auto Insurance Company took a random sample of 380 insurance claims paid out during a 1-year period. The average claim paid was $1580. Assume σ = $268.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

This problem is based on problems 11.4 & 11.5 from Lomax & Hahs-Vaughn, 3rd ed.

The following three independent random samples are obtained from three normally distributed populations with equal variance. The dependent variable is starting hourly wage, and the groups are the types of position (internship, co-op, work study).

Do not forget to convert this table from parallel format (i.e., groups in each column) to serial format for analysis in SPSS.

Use SPSS (or another statistical software package) to conduct a one-factor ANOVA to determine if the group means are equal using α=0.02α=0.02. Though not specifically assessed here, you are encouraged to also test the assumptions, plot the group means, and interpret the results.

Group means (report to 2 decimal places):
Group 1: Internship:   
Group 2: Co-op:   
Group 3: Work Study:   


ANOVA summary statistics:
F-ratio =
(report accurate to 3 decimal places)
p=p=
(report accurate to 4 decimal places)

Conclusion:

• The sample data suggest the average starting hourly wages are not the same.
• There is not sufficient data to conclude the starting wages are different for the different groups.

Is there a relationship between the number of stories a building has and its height? Some statisticians compiled data on a set of n = 52 buildings reported in the 1994 World Almanac. You will use the data set to decide whether height can be predicted from the number of stories. (a) Load the data from buildings.txt (Note that this is a text file, so use the appropriate instruction. If you are having trouble uploading the data, open it to see its contents and type the data in: one vector for heights and one vector for stories. Ignore the year data.) (b) Draw a scatterplot with stories in the x-axis and height in the y-axis. Does there seem to be a linear relationship between the two variables? (c) Find the linear correlation coefficient between these variables. What does it tell you about the linear relationship? (d) Obtain the linear model and summary. Write down the regression equation that relates height with stories. Add the line to the scatterplot. (e) Test for significance of the regression at  = 0.05. State the null and alternative hypotheses. Can the model be used for predictions? Justify your conclusion using the summary in (d). (f) State the coefficient of determination. What percentage of variation in height is explained by the number of stories? (g) Draw diagnostic plots (a plot of stories vs. residuals, and a normal probability plot for the residuals). Do assumptions appear to be satisfied?

YEAR    Height  Stories
1990    770     54
1980    677     47
1990    428     28
1989    410     38
1966    371     29
1976    504     38
1974    1136    80
1991    695     52
1982    551     45
1986    550     40
1931    568     49
1979    504     33
1988    560     50
1973    512     40
1981    448     31
1983    538     40
1968    410     27
1927    409     31
1969    504     35
1988    777     57
1987    496     31
1960    386     26
1984    530     39
1976    360     25
1920    355     23
1931    1250    102
1989    802     72
1907    741     57
1988    739     54
1990    650     56
1973    592     45
1983    577     42
1971    500     36
1969    469     30
1971    320     22
1988    441     31
1989    845     52
1973    435     29
1987    435     34
1931    375     20
1931    364     33
1924    340     18
1931    375     23
1991    450     30
1973    529     38
1976    412     31
1990    722     62
1983    574     48
1984    498     29
1986    493     40
1986    379     30
1992    579     42

*********************************

Need R console code

1). Calculate the specific correlation coefficient for this data. What does r_xy = ? You can use the table on the last page for your calculations (This is the tough one).

2). Does there appear to be a correlation between these two variables? If yes, in what direction (positive or negative)?

3). What are three possible explanations for this correlational relationship? (Note – These can include “third variable” explanations).

Fewer young people are driving. In year A, 67.9% of people under 20 years old who were eligible had a driver's license. Twenty years later in year B that percentage had dropped to 44.7%. Suppose these results are based on a random sample of 1,700 people under 20 years old who were eligible to have a driver's license in year A and again in year B.

(a)

At 95% confidence, what is the margin of error of the number of eligible people under 20 years old who had a driver's license in year A? (Round your answer to four decimal places.)

At 95% confidence, what is the interval estimate of the number of eligible people under 20 years old who had a driver's license in year A? (Round your answers to four decimal places.)

to

(b)

At 95% confidence, what is the margin of error of the number of eligible people under 20 years old who had a driver's license in year B? (Round your answer to four decimal places.)

At 95% confidence, what is the interval estimate of the number of eligible people under 20 years old who had a driver's license in year B? (Round your answers to four decimal places.)

to

(c)

Is the margin of error the same in parts (a) and (b)? Why or why not?

The margin of error in part (a) is  ---Select--- smaller larger than the margin of error in part (b). This is because the sample proportion of eligible people under 20 years old who had a driver's license in year B is  ---Select--- closer to 0 closer to 0.5 closer to 1 than the sample proportion of eligible people under 20 years old who had a driver's license in year A. This leads to a  ---Select--- smaller larger interval estimate in part (b).

The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting the systolic reading be the independent​ (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 150. Is the predicted value close to 66.2​, which was the actual diastolic​ reading? Use a significance level of 0.05.
Systolic
139
118
145
133
141
138
139
136
  
Diastolic
101
61
82
74
104
79
74
74
LOADING... Click the icon to view the critical values of the Pearson correlation coefficient r.

A simple linear least squares regression of the heights (in feet) of a building on the number of stories in the building was performed using a random sample of 30 buildings. The associated ANOVA F statistic was 5.60. What is the P-value associated with this ANOVA F test?

a.) greater than 0.10

b.) between 0.001 and 0.01

c.) between 0.01 and 0.025

d.) between 0.05 and 0.10

e.) between 0.025 and 0.05

f.) less than 0.001

The number of computers per household in a small town Computers 0 1 2 3 Households 298 284 97 18

Find probability distribution

Graph using a histogram

Describe distribution shape

Please solve using EXCEL SOLVER and show steps

1 – A company requires during the next four months, respectively, 50, 65, 100, and 70 units of a commodity (no backlogging is allowed). Production costs are $5, $8, $4, and $7 per unit during these months. The storage cost from one month to the next is $2 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 could be sold for $6. Formulate an LP that will minimize that the net cost incurred in meeting the demands of the next four months. Solve the problem using Solver by Excel.  Find the range of values for production costs which the current basis remains optimal.

Hint: Decision variables are production during each month and inventory at the end of each month.

In 2018 in an attempt to improve the reputation of the Democratic People’s Republic of Korea (DPRK) lottery tickets were sold to people around the world. The grand prize of this lottery was a weekend with Kim Jung Un. During anevening with Kim Jung Un the lottery winner was offered a meal made from one of the lobsters in Kim Jung Un’s private lobster aquarium.(Which by the way are all Maine lobsters!) The average weight of the lobsters was 22 ounces and the standard deviation was 0.67 ounces. When a random lobster wastaken from Kim Jung Un’s aquarium what was the probability it weighed more than 23.75 ounces?
a.) 0.0154 b.) 0.9955 c.) 0.9846 d.) 0.0045 e.)None of these

In lieu of using a single resistor three resistors are wired in series. The three resistors are identical. The resistance o f each is normally distributed with a mean of 6 ohms and a standard deviation of 0.3 ohms. The probability the combined resistance will exceed 19 ohm's is 0.0274. How precise (i.e. what is the required value of the standard deviation) would the manufacturing process have to be make the probability less than 0.0055 that t he combined resistance of the circuit would exceed 19 ohms?
a.) 0.180 ohms b.) 0.220 ohms c.) 0.227 ohms d.) 0.229 ohms e.) None of these

An experiment has two possible outcomes: the first occurs with probability p ; the second with probability p^2 . What is p?
a.) 0.3820 b.) 0.5000    c.) 0.2500     d.)   0.6180 e.) None of the above

Of all 3–to–5year old children, 56% are enrolled in school. If a sample of 500 such children is randomly selected, find the probability that at least 250 will be enrolled in school.Hint: Use De Moivre–Laplace.
a.) 0.9970 b.) 0.0035 c.) 0.9965 d.) 0.0030 e.) None of the above