A researcher believes that among the residents of a remote community, 30% have type O blood, 50% have type A blood, 10% have type B blood and 10% have type AB blood. She takes a random sample of 80 residents and finds that 20 had type O blood, 40 had type A blood, 12 had type B blood and 8 had type AB blood. Do the data follow the hypothesized distribution of blood type for this community? Test at a = .05. Round your answers to three decimal places, if necessary. Null hypothesis: Ho: Po= 0.3, PA = 0.5, PB = 0.1, PAB = 0.1 20 80 1 Ho: Po = Ho: Po = Type O -8 Alternative hypothesis: Ha: Po 20 20 PA = 1 Ho: Po = PA = PB = PAB = 4 Type O › PA = 24 0.667 Complete the table of observed counts: 40 80 1 40 PA #PB = PAB = 40 Ha: po 20 80' PA # Ha: Po 0.3, PA # 0.5, PB At least one of the proportions is different. Type A 40 ,PB = PB = Type A What is the test statistic? 2.667 40 PB # 80' Type A 0 1 2612 80 What is the critical value for this test? > How many degrees of freedom are there? 3 > Complete the table of expected counts under the null hypothesis: 12 8 80 80 0.1, PAB # 0.1 PAB = 2 PAB = 2.000 Type B PAB # 12 8 Type B 8 80 1 8 Using your previous answers, complete the table of contributions to the test statistic: Hint: Think about the formula for the test-statistic for a goodness of fit test. Type 0 Type B 8 Type AB Type AB 8 Type AB 0 Using your answer from the previous questions, find the p-value. 0.0446 Enter an integer or decimal number, accurate to at least 3 decimal places [more..] ▼ Part 2 of 5 Part 3 of 5 Part 4 of 5
A researcher believes that among the residents of a remote community, 30% have type O blood, 50% have type A blood, 10% have type B blood and 10% have type AB blood. She takes a random sample of 80 residents and finds that 20 had type O blood, 40 had type A blood, 12 had type B blood and 8 had type AB blood. Do the data follow the hypothesized distribution of blood type for this community? Test at a = .05. Round your answers to three decimal places, if necessary. Null hypothesis: Ho: Po= 0.3, PA = 0.5, PB = 0.1, PAB = 0.1 20 80 1 Ho: Po = Ho: Po = Type O -8 Alternative hypothesis: Ha: Po 20 20 PA = 1 Ho: Po = PA = PB = PAB = 4 Type O › PA = 24 0.667 Complete the table of observed counts: 40 80 1 40 PA #PB = PAB = 40 Ha: po 20 80' PA # Ha: Po 0.3, PA # 0.5, PB At least one of the proportions is different. Type A 40 ,PB = PB = Type A What is the test statistic? 2.667 40 PB # 80' Type A 0 1 2612 80 What is the critical value for this test? > How many degrees of freedom are there? 3 > Complete the table of expected counts under the null hypothesis: 12 8 80 80 0.1, PAB # 0.1 PAB = 2 PAB = 2.000 Type B PAB # 12 8 Type B 8 80 1 8 Using your previous answers, complete the table of contributions to the test statistic: Hint: Think about the formula for the test-statistic for a goodness of fit test. Type 0 Type B 8 Type AB Type AB 8 Type AB 0 Using your answer from the previous questions, find the p-value. 0.0446 Enter an integer or decimal number, accurate to at least 3 decimal places [more..] ▼ Part 2 of 5 Part 3 of 5 Part 4 of 5
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Blood Type Distribution Hypothesis Test**
A researcher investigates the distribution of blood types in a remote community. She hypothesizes the following proportions based on the general population: 30% with type O, 50% with type A, 10% with type B, and 10% with type AB blood. A sample of 80 residents revealed: 20 had type O, 40 had type A, 12 had type B, and 8 had type AB blood. The question is whether these results align with the hypothesized distribution at a significance level of 0.05.
### Null Hypothesis (H₀):
- \( p_O = p_A = p_B = p_{AB} = \frac{1}{4} \)
### Alternative Hypothesis (Hₐ):
- At least one of the proportions is different.
### Observed Counts:
- **Type O:** 20
- **Type A:** 40
- **Type B:** 12
- **Type AB:** 8
### Expected Counts (Under H₀):
- **Type O:** 24
- **Type A:** 40
- **Type B:** 8
- **Type AB:** 8
### Contributions to the Test Statistic:
- **Type O:** 0.667
- **Type A:** 0
- **Type B:** 2.000
- **Type AB:** 0
### Test Statistic Value:
- \( 2.667 \)
### Degrees of Freedom:
- \( 3 \)
### P-Value:
- \( 0.044 \)
This analysis uses a chi-square goodness of fit test to compare the observed and expected blood type distributions in the community.
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