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Question: A distribution and the observed frequencies of the values of a variable from a simple random samp...
A distribution and the observed frequencies of the values of a variable from a simple random sample of the population are provided below. Use the? chi-square goodness-of-fit test to? decide, at the specified significance? level, whether the distribution of the variable differs from the given distribution.
Distribution: 0.2, 0.1, 0.1,0.2,0.4
Observed? frequencies: 14, 7, 44, 11,14
Significance level=0.10
i. Compute the value of the test statistic, chisquare
ii. Identify the P value
iii. Does the data provide sufficient evidence that the distribution of the variable differs from the given distribution?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Ho: The proportions are 0.2, 0.1, 0.1, 0.2, 0.4
:
H1: At least one of the proportions in Ho: is false
:
Degrees of Freedom(DF) = 5 - 1 = 4
:
The number of observations in the sample is 14 +7 +44 + 11 +14 = 90
:
The expected frequency counts are
:
E(1) = 0.2 * 90 = 18
:
E(2) = 0.1 * 90 = 9
:
E(3) = 0.1 * 90 = 9
:
E(4) = 0.2 * 90 = 18
:
E(5) = 0.4 * 90 = 36
:
chi^2 test statistic = summation i = 1, 5 of [((O(i) - E(i))^2/E(i)] where O(i) is the observed frequency count
:
chi^2(X) = ((14-18)^2/18) +((7-9)^2/9) ((44-9)^2/9) +((11-18)^2/18) +((14-36)^2/36) = 77.55
:
Use a Chi-Square Distribution Calculator to find P(X > 77.55) = 0
:
Since the P-value (0) is less than the significance level (0.10), we cannot accept the null hypothesis.
:
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