Discussion Board 14 – Hypothesis Testing – Goodness of Fit (GOF) & Test of Indep

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Discussion Board 14 – Hypothesis Testing – Goodness of Fit (GOF) & Test of Independence (TOI)
1. You would like to see if the proportion of people who place orders at a specific time has changed since the end of spring at the local diner. Below is a table of the latest orders placed at the local diner (hypothesized – orders placed end of summer) random sample of 400 orders. Construct a hypothesis test, complete the table below as well as answering the questions asked of the discussion board. Use a level of significance of .05.
Hypothesis
Time
Proportion
Observed
Expected
Chi^2
6:00 to 7:30
0.20
90
7:30 to 9:00
0.30
100
9:00 to 10:30
0.15
70
Q 1 – A
10:30 to 12:00
0.25
110
12:00 to 1:30
0.10
30
Q 1 – B
Chi^2
9.750
A. What is the expected value for the 9:00 to 10:30 slot?
B. What is the value of the chi square test statistic for the 12:00 to 1:30 slot (round to the nearest tenth)? C. What is the probability of the test statistic for this specific problem?
D. 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.
E. Using the critical value approach at what critical value will you start rejecting the null hypothesis? 2. You would like to see if the Time Slot is independent of the Age Group. Construct a hypothesis test, complete the expected and chi square tables as well as answering the questions asked of the discussion board. Use a level of significance of .05.
Observed:
16-24
25-49
50+
7:00 – 10:00 am
10
20
20
50
10:00 – 1:00 pm
20
30
50
100
1:00 – 4:00 pm
30
30
30
90
4:00 – 7:00 pm
20
20
20
60
80
100
120
300
Expected:
16-24
25-49
50+
7:00 – 10:00 am
10:00 – 1:00 pm
Q2-A 1:00 – 4:00 pm
4:00 – 7:00 pm
Chi^2
16-24
25-49
50+
7:00 – 10:00 am
10:00 – 1:00 pm
1:00 – 4:00 pm
4:00 – 7:00 pm
Q2-B Chi^2=10.167 A. What is the expected value for 10-1pm & 50+ (Q1-A)? B. What is the value of the chi square test statistic for 4-7pm & 25-49 (Q1-B)? C. What is the probability of the test statistic for this specific problem?
D. 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.
E. 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 Monday, August 5th by 11PM.
When you answer the question put the answers in this order and label like this:
1A.
1B.
1C.
1D.
1E. 2A. 2B. 2C.
2D.
2E.

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