1. The Excel file Stock Data contains monthly data for several stocks and the S&P 500 Index (i.e., the market).
   1. Compute Beta for NT and the S & P 500 using the Covariance/Variance relationship.
   2. Compute Beta for NT and the S & P 500 using the EXCEL slope function.
   3. Compute the equation: R_i= a_i + b_iR_MKT for NT.
      1. Compute R² for this equation.
      2. Compute the t-statistic for a.
         1. Is the t-statistic for a Significant or Not Significant?
      3. Compute the t-statistic for β.
         1. Is the t-statistic for β Significant or Not Significant?

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 72 and estimated standard deviation σ = 41. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)


(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.

The probability distribution of x is not normal.The probability distribution of x is approximately normal with μ_x = 72 and σ_x = 20.50.    The probability distribution of x is approximately normal with μ_x = 72 and σ_x = 28.99.The probability distribution of x is approximately normal with μ_x = 72 and σ_x = 41.

What is the probability that x < 40? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)


(e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?

YesNo    

An IQ test scoring is designed to have mean of 100 and a standard deviation of 15. The scores are known to be normally distributed. A principal at a private school wants to investigate whether the average IQ of the students at her school is statistically different from the designed mean. She randomly samples from the school and has 15 students take the IQ test. The average test score of the sample is 95 and the sample standard deviation is 2. Use α = .10

1. Follow the 7 steps for hypothesis testing to solve this problem using the critical region method.

2. Calculate the p value.

3. Calculate the 90% confidence interval. Look to see if the hypothesized mean is in confidence intervals.

4. Do you come to the same conclusion using critical region, p value and confidence intervals?

Visit the NASDAQ historical prices weblink. First, set the date range to be for exactly 1 year ending on the Monday that this course started. For example, if the current term started on April 1, 2018, then use April 1, 2017 – March 31, 2018. (Do NOT use these dates. Use the dates that match up with the current term.) Do this by clicking on the blue dates after “Time Period”. Next, click the “Apply” button. Next, click the link on the right side of the page that says “Download Data” to save the file to your computer.

This project will only use the Close values. Assume that the closing prices of the stock form a normally distributed data set. This means that you need to use Excel to find the mean and standard deviation. Then, use those numbers and the methods you learned in sections 6.1-6.3 of the course textbook for normal distributions to answer the questions. Do NOT count the number of data points.

Complete this portion of the assignment within a single Excel file. Show your work or explain how you obtained each of your answers. Answers with no work and no explanation will receive no credit.

1. a) Submit a copy of your dataset along with a file that contains your answers to all of the following questions.

b) What the mean and Standard Deviation (SD) of the Close column in your data set?

c) If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? Hint: You do not want to calculate the mean to answer this one. The probability would be the same for any normal distribution.

2. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at more than $950?
3. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed within $50 of the mean for that year? (between 50 below and 50 above the mean)
4. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than $800 per share. Would this be considered unusal? Use the definition of unusual from the course textbook that is measured as a number of standard deviations
5. At what prices would Google have to close in order for it to be considered statistically unusual? You will have a low and high value. Use the definition of unusual from the course textbook that is measured as a number of standard deviations
6. What are Quartile 1, Quartile 2, and Quartile 3 in this data set? Use Excel to find these values. This is the only question that you must answer without using anything about the normal distribution.
7. Is the normality assumption that was made at the beginning valid? Why or why not? Hint: Does this distribution have the properties of a normal distribution as described in the course textbook? Real data sets are never perfect, however, it should be close. One option would be to construct a histogram like you did in Project 1 to see if it has the right shape. Something in the range of 10 to 12 classes is a good number.

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test. H0: p=0.91 versus H1: p≠0.9

Thirty-one small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 44.5 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error increases.As the confidence level increases, the margin of error remains the same.    As the confidence level increases, the margin of error decreases.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval decreases in length.As the confidence level increases, the confidence interval increases in length.    As the confidence level increases, the confidence interval remains the same length.

1. In a random sample of male and female New York street performers between the ages of 22-35 you know that:

The probability a man is a mime is 0.30.

the probability a woman is a spray paint artist is 0.165

The probability a man is a break dancer; given that he’s a mime is 0.250.

The probability a woman is a faux statue is 0.550.

The probability a woman is a faux statue, given that she’s a spray paint artist is .065.

Compute the following probabilities: (6 points: 2 points for each problem)

a.P(woman is a spray paint artist and a faux statue)

b.P (woman is a spray paint artist or a faux statue)



c.P (man is a mime and a break dancer)

you draw a single card from a standard 52-card deck. find the probability of each event. simplify the probability ratio or write in decimal form. a) ace or a nine b) not a king c) club or a face card d) spade or a heart e) neither a diamond nor a 7

Describes at least 5 differences between the interpretation of results from an efficacy study and an effectiveness study (Minimum 300 words)

The major stock market indexes had strong results in 2014. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies was +11.4%. The mean one year return for the NASDAQ, a group of 3200 small and medium-sized companies was +13.4%. Historically, the one-year returns are approximately normal, the standard deviation in the S&P 500 is approximately 20% and the standard deviation in NASDAQ is approximately 30%.

1. What is the probability that a stock in the S&P 500 gained value in 2014?
2. What is the probability that a stock in the S&P 500 gained 10% or more in 2014?
3. What is the probability that a stock in the S&P 500 lost 20% or more in 2014?
4. What is the probability that a stock in the S&P 500 lost 30% or more in 2014?
5. Repeat (a) through (d) for a stock in the NASDAQ.
6. Write a short report on your findings Be sure to include a discussion on the risks associated with a large standard deviation. How would you use the findings to provide advice on investing in the S&P 500 or NASDAQ stock market?

Please explain how you get the answer to x (or Z) step by step

The following example comes from Statistics: Concepts and Controversies, by David Moore and William Notz.

Find an example of one of the following:

1. Leaving out essential information

2. Lack of consistency

3. Implausible numbers

4. Faulty Arithmetic

Explain in detail the statistical shortcomings of your example.

Please give an example of when using the probability an event will occur is important to decision making.  Why?

Suppose x has a distribution with μ = 23 and σ = 18.

(a) If a random sample of size n = 42 is drawn, find μ_x, σ_x and P(23 ≤ x ≤ 25). (Round σ_x to two decimal places and the probability to four decimal places.)

(b) If a random sample of size n = 63 is drawn, find μ_x, σ_x and P(23 ≤ x ≤ 25). (Round σ_x to two decimal places and the probability to four decimal places.)

(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)
The standard deviation of part (b) is  ---Select--- smaller than larger than the same as part (a) because of the  ---Select--- larger smaller same sample size. Therefore, the distribution about μ_x is  ---Select--- wider narrower the same .

Assume that a sample is used to estimate a population mean μμ. Find the 99.5% confidence interval for a sample of size 642 with a mean of 22.2 and a standard deviation of 9.3. Enter your answers accurate to four decimal places.

Confidence Interval = ( , )

You measure 29 textbooks' weights, and find they have a mean weight of 47 ounces. Assume the population standard deviation is 10.8 ounces. Based on this, construct a 99.5% confidence interval for the true population mean textbook weight.

Keep 4 decimal places of accuracy in any calculations you do. Report your answers to four decimal places.

Confidence Interval = ( , )