Question

In: Statistics and Probability

A university surveyed recent graduates of the English department for their starting salaries. Three hundred graduates...

A university surveyed recent graduates of the English department for their starting salaries. Three hundred graduates returned the survey. The average salary was $25,000. The sample standard deviation was $1,500. What is the 95% confidence interval for the mean salary of all graduates from the English department?

Solutions

Expert Solution

Solution :

Given that,

= $25000

s =$1500

n =300

Degrees of freedom = df = n - 1 = 300- 1 = 299

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,299 = 1.968 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 1.968 * (1500 / 300)

= 170.4338

The 95% confidence interval estimate of the population mean is,

- E < < + E

25000- 170.4338 < < 25000+ 170.4338

24829.5662 < < 25170.4338

( 24829.5662 ,25170.4338)

orchestra answered 1 year ago
Next > < Previous

Related Solutions

A university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates...
A university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. The population standard deviation was $2,500. What is the 90% confidence interval for the mean salary of all graduates from the English Department? A) [$24,794, $25,206] B) [$24,988, $25,012] C) [$22,500, $27,500] D) [$24,755, $25,245]
Suppose that salaries of recent graduates from a large state university are normally distributed with mean...
Suppose that salaries of recent graduates from a large state university are normally distributed with mean $45,000 and standard deviation $4,200. (1) What proportion of salaries are between $40,000 and $55,000? (2) What two salaries bound the middle 40%?
2. Starting salaries. You are planning a survey of starting salaries for recent computer science majors....
2. Starting salaries. You are planning a survey of starting salaries for recent computer science majors. In the latest survey by the National Association of Colleges and Employers, the average starting salary was reported to be $61,287. If you assume that the standard deviation is $3850, what sample size do you need to have a margin of error equal to $500 with 95% confidence? (report as an integer) 3. Suppose that in the setting of question 2 you have resources...
1. Assume that the starting salaries for the Class of 2013 college graduates is (rounded, in...
1. Assume that the starting salaries for the Class of 2013 college graduates is (rounded, in $1000’s) normally distributed with µ = 45 and σ = 5. (Based on real data.) a. Sketch and label the normal curve. b. In what range must a starting salary be for a graduate to be in (approximately) the highest 16% ? c. In what range must a starting salary be for a graduate to be in (approximately) the lowest .15% ? d. In...
Assume that 40% of graduates come from University A and and earn salaries of 30,000 on...
Assume that 40% of graduates come from University A and and earn salaries of 30,000 on average with a standard deviation of 5,000. The remainder come from University B and earn salaries of 25,000 on average with a standard deviation of 7,500. If you are told that a graduate is earning less than 35,000, what is the probability that they came from University A? (Assume salaries are normally distributed.)
Annual starting salaries for college graduates with degrees in business administration are generally expected to be...
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. Given the information in the Microsoft Excel Online file below, construct a spreadsheet to determine how large a sample should be taken for each desired margin of error. For a margin of error of ± $400 , the required sample size is n =...
Annual starting salaries for college graduates with degrees in business administration are generally expected to be...
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $40,000 and $54,200. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. (Round your answers up to the nearest whole number.) What is the planning value for the population standard deviation? (a) How large a sample should be taken if the desired margin of error is $600? (b) How large a sample should be taken if...
Annual starting salaries for college graduates with degrees in business administration are generally expected to be...
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $10,000 and $50,000. Assume that a confidence interval estimate of the population mean annual starting salary is desired. a. What is the planning value for the population standard deviation? b. How large a sample should be taken if the desired margin of error is $500? Round your answer to next whole number. $230? $140?
Annual starting salaries for college graduates with degrees in business administration are generally expected to be...
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $10,000 and $50,000 . Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. a. What is the planning value for the population standard deviation? = ________ b. How large a sample should be taken if the desired margin of error is $400? Round your answer to next whole number. _________
Annual starting salaries for college graduates with degrees in business administration are generally expected to be...
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $33,000 and $48,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. (Round your answers up to the nearest whole number.) 1) What is the planning value for the population standard deviation? 2) How large a sample should be taken if the desired margin of error is $600? 3) How large a sample should be taken...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT