study was conducted to verify the age distribution among residents in suburban areas. There were k = 6 age groups selected for this study. The observed frequencies and theoretical proportions under the null hypothesis are shown in the table below. Age Group Under 20 [20, 30) [30, 40) [40, 50) [50, 65) 65 and Above Total Frequency 132 148 224 62 188 Proportions 0.15 0.20 0.25 0.10 0.25 0.05 007 08 0h 007 091 011 008 1. Determine all counts expected under the null hypothesis and place them into the table above 2. Evaluate the test statistic Solution (224-200)2 091 (46-40) 0.9 24,05 22-200)? 20,22

MATLAB: An Introduction with Applications
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Demographic study was conducted to verify the age distribution among residents in suburban areas. There
were k = 6 age groups selected for this study. The observed frequencies and theoretical proportions under
the null hypothesis are shown in the table below.
Age Group
Under 20 [20, 30) [30, 40) [40, 50) [50, 65) 65 and Above
Total
Frequency
132
148
224
62
188
Proportions
0.15
0.20
0.25
0.10
0.25
0.05
008
007. 08
EXPECTED
007 091
1. Determine all counts expected under the null hypothesis and place them into the table above
2. Evaluate the test statistic
१/०ग -h00)
2 2.88
Solution
091
162-80)4.05
200)2
20,22
(46-40) 0.9
Transcribed Image Text:Demographic study was conducted to verify the age distribution among residents in suburban areas. There were k = 6 age groups selected for this study. The observed frequencies and theoretical proportions under the null hypothesis are shown in the table below. Age Group Under 20 [20, 30) [30, 40) [40, 50) [50, 65) 65 and Above Total Frequency 132 148 224 62 188 Proportions 0.15 0.20 0.25 0.10 0.25 0.05 008 007. 08 EXPECTED 007 091 1. Determine all counts expected under the null hypothesis and place them into the table above 2. Evaluate the test statistic १/०ग -h00) 2 2.88 Solution 091 162-80)4.05 200)2 20,22 (46-40) 0.9
Use summaries obtained from the study described in the previous problem.
Conduct a goodness-of-fit test and provide detailed explanations for your decision in each case
1. At the significance level a = 0.05, do you have evidence that the true distribution would deviate
from the hypothetical one?
• Show the critical value
• Formulate the rejection rule
• State your decision
2. Repeat this procedure at the significance level a = 0.10
• Show the critical value
• Formulate the rejection rule
• State your decision
Solution
8
Transcribed Image Text:Use summaries obtained from the study described in the previous problem. Conduct a goodness-of-fit test and provide detailed explanations for your decision in each case 1. At the significance level a = 0.05, do you have evidence that the true distribution would deviate from the hypothetical one? • Show the critical value • Formulate the rejection rule • State your decision 2. Repeat this procedure at the significance level a = 0.10 • Show the critical value • Formulate the rejection rule • State your decision Solution 8
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