iscussion Board 13 – CI & Hyp – Single Pop Std Dev & Var – & Hyp – Two Independe

iscussion Board 13 – CI & Hyp – Single Pop Std Dev & Var – & Hyp – Two Independent Population Standard Deviation

1. You would like to construct a confidence interval for the standard deviation for the time it takes to prepare a tax return. You randomly select 70 tax returns and get a sample standard deviation of 8.3 minutes. Construct a 90% confidence interval for the standard deviation for the time it takes to prepare a tax return.

(Round margin of error to 3 decimal places at the end) and (express the final answer with 3 decimal places- such as 7.123 to 15.246). Make sure to use values from your tables. Test statistics, confidence interval values and probabilities generated by your calculator should not be used. © Chris O’Byrne 2024

2. Last year (Tax Year 2022), the standard deviation of tax return refunds was $1,140. You would like to see if the standard deviation (variability) has increased this tax season (2023). You randomly select 35 tax returns with refunds and get a standard deviation of $1,275. Conduct a hypothesis test to see if the standard deviation (variability) has increased this tax season and use a level of significance of .05. © Chris O’Byrne 2024

A. What is the test statistics value (correct number of decimal places depending on which test statistic)?

B. What is the probability of the test statistic for this specific problem? (take into consideration if this is 1-tail or 2-tail test)

C. What conclusion will you come to? (just need to state Accept Ho or Reject Ho and Accept Ha – just put one of those 2 answers in the body of the discussion board, but you will have a more detailed solution (besides writing one of these statements you will write out in words what the conclusion means) on your worksheet that you will attach as a PDF). Use a level of significance of .05.

D. Using the critical value approach at what critical value or values will you start rejecting the null hypothesis? (make sure you are very careful and detailed with your answer, pay attention to signs and values)

3. You would like to see if the standard deviation (variability) of the earnings of stocks for the NASDAQ is greater than the standard deviation of the earnings of stocks for the S&P 500 for this current year. Use the information below and do a hypothesis test to see if the standard deviation (variability) of the earnings of stocks for the NASDAQ is greater than the standard deviation of the earnings of stocks for the S&P 500 for this current year. Use a level of significance of .05.

NASDAQS&P 500

45.3Sample Standard Deviation 37.1

30Sample Size45

A. What is the test statistics value (correct number of decimal places depending on which test statistic)?

B. What is the probability of the test statistic for this specific problem? (take into consideration if this is 1-tail or 2-tail test)

C. What conclusion will you come to? (just need to state Accept Ho or Reject Ho and Accept Ha – just put one of those 2 answers in the body of the discussion board, but you will have a more detailed solution (besides writing one of these statements you will write out in words what the conclusion means) on your worksheet that you will attach as a PDF). Use a level of significance of .05.

D. Using the critical value approach at what critical value will you start rejecting the null hypothesis?

© Chris O’Byrne 2024

**** Use the appropriate table or tables from our lecture notes to answer all questions that require values or probabilities***** © Chris O’Byrne 2024

***No probabilities generated from a calculator will be permitted/accepted (will not receive credit), only probabilities and values from your Z-tables (CH6), T-tables (CH8) and Chi Square (CH11) and F-tables (CH11) notes will be allowed. ***

When doing and showing your work for the PDF – it should be handwritten as if you are figuring out the problem on the exam – it doesn’t need to be typed up – and I prefer that you DON’T type it out and that you hand write it.

This Discussion Board is Due Friday, August 2nd by 11PM.

When you answer the question put the answers in this order and label like this:

1.

2A.

2B.

2C.

2D.

3A.

3B.

3C.

3D.