Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.8.

(a) Use the Normal approximation to find the probability that Jodi scores 74% or lower on a 100-question test. (Round your answer to four decimal places.)

(b) If the test contains 250 questions, what is the probability that Jodi will score 74% or lower? (Use the normal approximation. Round your answer to four decimal places.)

(c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?

The market and Stock J have the following probability distributions:

Calculate the expected rate of return for the market. Round your answer to two decimal places.

Calculate the expected rate of return for Stock J. Round your answer to two decimal places.

Calculate the standard deviation for the market. Do not round intermediate calculations. Round your answer to two decimal places.

Calculate the standard deviation for Stock J. Do not round intermediate calculations. Round your answer to two decimal places.

Consider the following probability distribution for Stock Fund (S) and Bond Fund (B).

The expected return and the standard deviation of the Stock Fund are 12% and 18.33%, respectively.

What is the expected return of Bond Fund?

What is the standard deviation of Bond Fund?

What is the covariance between the Stock Fund and the Bond Fund?

What is the correlation coefficient between the Stock Fund and the Bond Fund?

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 March 18, 2018 - March 17, 2019.) 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. 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 $1150? (5 points)
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 within $50 of the mean for that year? (Hint: this means the probability of being between 50 below and 50 above the mean) (5 points)
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 at less than $900 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 points)
4. 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. (5 points)
5. 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. (5 points)
6. 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. (5 points)

(Choose Best Option)

1) The probability of a type I error increases when:

a) Significance is lowered b) The number of samples is lowered c) Using two-tailed t-test rather than a one-tailed t-test d) Multiple pair-wise comparisons are performed

2) A population has a mean weight of 70 kg with a standard deviation of 5 kg. The weight of a sample of N = 100 subjects were taken. The following statement is false:

a) 95% of the people in the population have a weight between 60 kg and 80 kg b) There is a 95% probability that the sample mean is between 69 kg and 71 kg c) There is a 95% probability that the sample mean is between 69.5 kg and 71.5 kg d) The mean of the sampling distribution of the mean is exactly 70 kg.

3) The following statement is true:

a) It is easier to reject the null hypothesis if the researcher uses a smaller alpha (α) level b) You are more likely to make a Type I error when using a small sample than when using a large sample c) You accept the alternative hypothesis when you reject the null hypothesis d) As the sample size gets larger, the probability that the confidence interval will contain the population mean gets higher

4) The following statement is true:

a) The probability value is the probability that the null hypothesis is false. b) A researcher risks making a Type I error any time the null hypothesis is rejected c) A low probability value indicates a large effect. d) A non-significant outcome means that the null hypothesis is probably true.

5) The following increases power of a statistical test: a) A smaller sample size b) A higher population variance c) A higher alpha value d) Using two-tailed t-test rather than a one-tailed t-test 6) A paired t-test yields a p-value of p = 0.0001. Using this knowledge, the following is true:

a) There is large difference between the means of the two conditions b) The null hypothesis is false c) There is a high probability that the alternate hypothesis is true d) The test has high power

(Choose Best Option)

1) The probability of a type I error increases when:
a) Significance is lowered
b)   The number of samples is lowered
c)   Using two-tailed t-test rather than a one-tailed t-test
d)   Multiple pair-wise comparisons are performed
 
2) A population has a mean weight of 70 kg with a standard deviation of 5 kg. The weight of a sample of N = 100 subjects were taken.

The following statement is false:
a)   95% of the people in the population have a weight between 60 kg and 80 kg
b)   There is a 95% probability that the sample mean is between 69 kg and 71 kg
c)   There is a 95% probability that the sample mean is between 69.5 kg and 71.5 kg
d)   The mean of the sampling distribution of the mean is exactly 70 kg.

3) The following statement is true:
a)   It is easier to reject the null hypothesis if the researcher uses a smaller alpha (α) level
b)   You are more likely to make a Type I error when using a small sample than when using a large sample
c)   You accept the alternative hypothesis when you reject the null hypothesis
d)   As the sample size gets larger, the probability that the confidence interval will contain the population mean gets higher

4) The following statement is true:
a)   The probability value is the probability that the null hypothesis is false.
b)   A researcher risks making a Type I error any time the null hypothesis is rejected
c)   A low probability value indicates a large effect.
d)   A non-significant outcome means that the null hypothesis is probably true.

5) The following increases power of a statistical test:
a)   A smaller sample size
b)   A higher population variance
c)   A higher alpha value
d)   Using two-tailed t-test rather than a one-tailed t-test

6) A paired t-test yields a p-value of p = 0.0001. Using this knowledge, the following is true:
a)   There is large difference between the means of the two conditions
b)   The null hypothesis is false
c)   There is a high probability that the alternate hypothesis is true
d)   The test has high power
 

Fund life & health insurance

Explain carefully why this statement is false

Since the level of insurer’s capital reflects its financial stability, companies with the highest absolute value of capital is always preferred.

Comment on the following statement: “It is always better to use as many instruments as possible in 2SLS. This allows to have the highest possible prediction accuracy of the endogenous variable” in the first step, and hence, provides gains in efficiency.

2)   Describe the symptoms associated with mild depression. What interventions would the nurse implement when evaluating/caring for a client with mild depression. List interventions in priority order (highest priority to lowest).

Which one of the following has the highest effective annual rate? 6 percent compounded annually 6 percent compounded semiannually 6 percent compounded quarterly 6 percent compounded daily