(S 12.1) Suppose there is a random sample of n observations, divided into four groups. The table below summarizes the count of observations that were seen in each group.
Group 1 |
Group 2 |
Group 3 |
Group 4 |
24 |
38 |
50 |
34 |
We are interested in testing the null hypothesis H0:p1=p2=p3=p4=0.25, against the alternative hypothesis HA:Atleastoneproportionisincorrect.
What is the expected count for each of the groups?
Expected:
What is the value of the test statistic? Round your response to at least 2 decimal places.
What are the appropriate degrees of freedom?
What is the P-value? Round to at least 4 decimal places
H0: p1 = p2 = p3 = p4 = 0.25
HA: At least one proportion is incorrect.
Level of significance = 0.05
Test statistic is
O: Observed frequency
E: Expected frequency.
E = n*pi
O | E | (O-E) | (O-E)^2 | (O-E)^2/E | |
24 | 36.5 | -12.5 | 156.25 | 4.280822 | |
38 | 36.5 | 1.5 | 2.25 | 0.061644 | |
50 | 36.5 | 13.5 | 182.25 | 4.993151 | |
34 | 36.5 | -2.5 | 6.25 | 0.171233 | |
Total | 146 | 9.51 |
Degrees of freedom = Number of E's - 1 = 4 - 1 = 3
P-value = P( ) = 0.0233
P-value < 0.05 we reject null hypothesis.
Conclusion:
At least one proportion is incorrect.
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