A researcher drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 209 times. The observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6 respectively are 31, 37, 43, 41, 20, and 37. Use a 0.05 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? O Determine the null and alternative hypotheses. Choose the correct answer below. O A. Ho: At least one of the probabilities is different from the others. Ha: All outcomes are equally likely. O B. Ho: All outcomes are equally likely. H: At least one of the probabilities is different from the others. O C. Ho: All frequencies are equal to 5. Ha: All frequencies are less than 5. O D. Ho: All frequencies are less than 5. Ha: All frequencies are equal to 5. Compute the value of the test statistic, y2. y2 = (Round to two decimal places as needed.) Find the P-value. P= (Round to three decimal places as needed.) Does it appear that the loaded die behaves differently than a regular die? O A. Yes, because there is not sufficient evidence to reject the null hypothesis. O B. No, because there is sufficient evidence to reject the null hypothesis. OC. No, because there is not sufficient evidence to reject the null hypothesis. O D. Yes, because there is sufficient evidence to reject the null hypothesis.
A researcher drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 209 times. The observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6 respectively are 31, 37, 43, 41, 20, and 37. Use a 0.05 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? O Determine the null and alternative hypotheses. Choose the correct answer below. O A. Ho: At least one of the probabilities is different from the others. Ha: All outcomes are equally likely. O B. Ho: All outcomes are equally likely. H: At least one of the probabilities is different from the others. O C. Ho: All frequencies are equal to 5. Ha: All frequencies are less than 5. O D. Ho: All frequencies are less than 5. Ha: All frequencies are equal to 5. Compute the value of the test statistic, y2. y2 = (Round to two decimal places as needed.) Find the P-value. P= (Round to three decimal places as needed.) Does it appear that the loaded die behaves differently than a regular die? O A. Yes, because there is not sufficient evidence to reject the null hypothesis. O B. No, because there is sufficient evidence to reject the null hypothesis. OC. No, because there is not sufficient evidence to reject the null hypothesis. O D. Yes, because there is sufficient evidence to reject the null hypothesis.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:A researcher drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 209 times. The observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6 respectively are 31, 37, 43, 41, 20, and 37. Use a 0.05 significance level
to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? O
.....
Determine the null and alternative hypotheses. Choose the correct answer below.
A. Ho: At least one of the probabilities is different from the others.
Ha: All outcomes are equally likely.
B. Ho: All outcomes are equally likely.
Ha: At least one of the probabilities is different from the others.
C. Ho: All frequencies are equal to 5.
Ha: All frequencies are less than 5.
D. Ho: All frequencies are less than 5.
Ha: All frequencies are equal to 5.
Compute the value of the test statistic, x2.
x² =
(Round to two decimal places as needed.)
Find the P-value.
P =
(Round to three decimal places as needed.)
Does it appear that the loaded die behaves differently than a regular die?
A. Yes, because there is not sufficient evidence to reject the null hypothesis.
B. No, because there is sufficient evidence to reject the null hypothesis.
C. No, because there is not sufficient evidence to reject the null hypothesis.
D. Yes, because there is sufficient evidence to reject the null hypothesis.
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