Question

In: Statistics and Probability

A factor in determining the usefulness of an examination as a measure of demonstrated ability is...

A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 29 newly graduated law students. Their scores give a sample standard deviation of 65 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60.

(f) Find a 99% confidence interval for the population variance. (Round your answers to two decimal places.)

lower limit
upper limit    


(g) Find a 99% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

lower limit points
upper limit     points

Solutions

Expert Solution

From the given data:s= 65, Therefore s2 = 4225, n = 29, and degrees of freedom = n - 1 = 28. = 0.01

We find critical values for /2 = 0.005 and 1- /2 = 1 – 0.995 = 0.975, df = 28

The lower critical value and the upper critical critical value

The confidence interval is given by:

Therefore:

Lower Limit = 2319.93

Upper Limit = 9493.62

___________________________________

(b) For the population standard deviation, we take the square root of the limits of the variance.

Therefore:

Lower Limit = Sqrt(2319.93) = 48.17

Upper Limit = Sqrt(9493.62) = 97.44

_____________________________________

orchestra answered 2 years ago
Next > < Previous

Related Solutions

A factor in determining the usefulness of an examination as a measure of demonstrated ability is...
A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state...
A factor in determining the usefulness of an examination as a measure of demonstrated ability is...
A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state...
A factor in determining the usefulness of an examination as a measure of demonstrated ability is...
A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state...
The statement of cash flows is not useful for:   a. Determining a company's ability to...
The statement of cash flows is not useful for:   a. Determining a company's ability to pay its debts.     b. Planning future investing and financing activities.     c. Determining a company's ability to pay dividends.     d. Calculating the net worth of a company.
Upon completion of this exercise, you will have demonstrated the ability to: Use C# loops Construct...
Upon completion of this exercise, you will have demonstrated the ability to: Use C# loops Construct conditions INTRODUCTION Your instructor will assign one of the following projects, each involves the user of loops and the construction of conditions to control them. CODING STANDARDS The following coding standards must be followed when developing your program: An opening documentation at the beginning of the source file describing the purpose, input, process, output, author, last modified date of the program. Write only one...
OBJECTIVE Upon completion of this exercise, you will have demonstrated the ability to: Use C# loops...
OBJECTIVE Upon completion of this exercise, you will have demonstrated the ability to: Use C# loops Construct conditions INTRODUCTION Your instructor will assign one of the following projects, each involves the user of loops and the construction of conditions to control them. CODING STANDARDS The following coding standards must be followed when developing your program: An opening documentation at the beginning of the source file describing the purpose, input, process, output, author, last modified date of the program. Write only...
Question 3 Define “productivity”. Compare single factor productivity measure with total factor productivity measure. What do...
Question 3 Define “productivity”. Compare single factor productivity measure with total factor productivity measure. What do we mean when we say productivity is a “relative” measure? Various financial data for the past two years follow. Calculate the total factor productivity and the single-factor productivity measures for labor, capital, and raw materials for this company for both years. What do these measures tell you about this company? Last Year This Year Output: Sales $201,005 $202,015 Inputs: Labor $30,010 $40,010 Raw materials...
Which of the following is not a factor in determining the required return on the bond?...
Which of the following is not a factor in determining the required return on the bond? a. Political risk b. liquidity risk c. default risk d. the inflation rate Which of the following statements is not true regarding beta? a:Beta is the ratio of a firm's systematic risk to the overall risk of the market b. a stock's risk premium depends upon its beta c. a stock with a beta of two will have a required return which is twice...
1)The ability to refinance short-term obligations on a long-term basis can be demonstrated if the company...
1)The ability to refinance short-term obligations on a long-term basis can be demonstrated if the company has already refinanced those obligations after the date of the balance sheet but before it is issued. True False   2) Which of the following statements does not describe an essential characteristic of a liability? The transaction or event obligating the enterprise has already occurred. The identity of the recipient must be known to the obligated party. The obligated entity has little or no discretion...
List three (3) factors that limit the usefulness of real GDP per person as a measure...
List three (3) factors that limit the usefulness of real GDP per person as a measure of the standard of living . Then discuss how these factors affect real GDP per person as a measure of living standards .
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT