Consider a multinomial experiment with n = 250 and k = 4. The null hypothesis to be tested is H0: p1 = p2 = p3 = p4 = 0.25. The observed frequencies resulting from the experiment are: (You may find it useful to reference the appropriate table: chi-square table or F table) Category 1 2 3 4 Frequency 70 42 72 66 a. Choose the appropriate alternative hypothesis. All population proportions differ from 0.25. Not all population proportions are equal to 0.25. b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) b-2. Find the p-value. p-value < 0.01 0.01 ≤ p-value < 0.025 0.025 ≤ p-value < 0.05 0.05 ≤ p-value < 0.10 p-value ≥ 0.10 c. At the 5% significance level, what is the conclusion to the hypothesis test? Reject H0 since the p-value is less than the significance level. Reject H0 since the p-value is greater than the significance level. Do not reject H0 since the p-value is greater than the significance level. Do not reject H0 since the p-value is less than the significance level.
Consider a multinomial experiment with n = 250 and k = 4. The null hypothesis to be tested is H0: p1 = p2 = p3 = p4 = 0.25. The observed frequencies resulting from the experiment are: (You may find it useful to reference the appropriate table: chi-square table or F table) Category 1 2 3 4 Frequency 70 42 72 66 a. Choose the appropriate alternative hypothesis. All population proportions differ from 0.25. Not all population proportions are equal to 0.25. b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) b-2. Find the p-value. p-value < 0.01 0.01 ≤ p-value < 0.025 0.025 ≤ p-value < 0.05 0.05 ≤ p-value < 0.10 p-value ≥ 0.10 c. At the 5% significance level, what is the conclusion to the hypothesis test? Reject H0 since the p-value is less than the significance level. Reject H0 since the p-value is greater than the significance level. Do not reject H0 since the p-value is greater than the significance level. Do not reject H0 since the p-value is less than the significance level.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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Question
Consider a multinomial experiment with n = 250 and k = 4. The null hypothesis to be tested is H0: p1 = p2 = p3 = p4 = 0.25. The observed frequencies resulting from the experiment are: (You may find it useful to reference the appropriate table: chi-square table or F table)
| Category | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Frequency | 70 | 42 | 72 | 66 |
a. Choose the appropriate alternative hypothesis.
-
All population proportions differ from 0.25.
-
Not all population proportions are equal to 0.25.
b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
b-2. Find the p-value.
-
p-value < 0.01
-
0.01 ≤ p-value < 0.025
-
0.025 ≤ p-value < 0.05
-
0.05 ≤ p-value < 0.10
-
p-value ≥ 0.10
c. At the 5% significance level, what is the conclusion to the hypothesis test?
-
Reject H0 since the p-value is less than the significance level.
-
Reject H0 since the p-value is greater than the significance level.
-
Do not reject H0 since the p-value is greater than the significance level.
-
Do not reject H0 since the p-value is less than the significance level.
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