Assume that it is reasonable to regard this sample of 91 home runs as representative of home runs hit at the stadium. Carry out a hypothesis test to determine if there is convincing evidence that the proportions of home runs hit are not the same for all five directions. Let p1, p2, p3, p4, and p5 be the proportions of home runs hit in the five directions. State the appropriate null and alternative hypotheses. H0: p1 = p2 = p3 = p4 = p5 = 0.2 Ha: H0 is not true. None of the proportions are equal to 0.2.H0: p1 = p2 = p3 = p4 = p5 = 0.5 Ha: H0 is not true. At least one of the proportions is not equal to 0.5. H0: p1 = p2 = p3 = p4 = p5 = 0.5 Ha: H0 is not true. None of the proportions are equal to 0.5.H0: None of the proportions are equal to 0.5. Ha: H0 is not true. p1 = p2 = p3 = p4 = p5 = 0.5H0: p1 = p2 = p3 = p4 = p5 = 0.2 Ha: H0 is not true. At least one of the proportions is not equal to 0.2. Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.) X2=P-value= State the conclusion in the problem context. Reject H0. There is convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions.Reject H0. There is not convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions. Do not reject H0. There is not convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions.Do not reject H0. There is convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions. (b) Describe how the observed counts for the five directions differ from what would have been expected if the proportions of home runs were the same for all five directions. For home runs going to left center and center field, the observed counts are significantly higher than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field, the observed count is much lower than the number that would have been expected.For home runs going to left center and center field, the observed counts are significantly lower than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field, the observed count is much higher than the number that would have been expected. For home runs going to left center and center field, the observed counts are significantly lower than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field the observed count is also much lower than the number that would have been expected.For home runs going to left center and center field, the observed counts are significantly higher than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field, the observed count is also much higher than the number that would have been expected.

Assume that it is reasonable to regard this sample of 91 home runs as representative of home runs hit at the stadium. Carry out a hypothesis test to determine if there is convincing evidence that the proportions of home runs hit are not the same for all five directions. Let p1, p2, p3, p4, and p5 be the proportions of home runs hit in the five directions. State the appropriate null and alternative hypotheses. H0: p1 = p2 = p3 = p4 = p5 = 0.2 Ha: H0 is not true. None of the proportions are equal to 0.2.H0: p1 = p2 = p3 = p4 = p5 = 0.5 Ha: H0 is not true. At least one of the proportions is not equal to 0.5. H0: p1 = p2 = p3 = p4 = p5 = 0.5 Ha: H0 is not true. None of the proportions are equal to 0.5.H0: None of the proportions are equal to 0.5. Ha: H0 is not true. p1 = p2 = p3 = p4 = p5 = 0.5H0: p1 = p2 = p3 = p4 = p5 = 0.2 Ha: H0 is not true. At least one of the proportions is not equal to 0.2. Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.) X2=P-value= State the conclusion in the problem context. Reject H0. There is convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions.Reject H0. There is not convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions. Do not reject H0. There is not convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions.Do not reject H0. There is convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions. (b) Describe how the observed counts for the five directions differ from what would have been expected if the proportions of home runs were the same for all five directions. For home runs going to left center and center field, the observed counts are significantly higher than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field, the observed count is much lower than the number that would have been expected.For home runs going to left center and center field, the observed counts are significantly lower than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field, the observed count is much higher than the number that would have been expected. For home runs going to left center and center field, the observed counts are significantly lower than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field the observed count is also much lower than the number that would have been expected.For home runs going to left center and center field, the observed counts are significantly higher than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field, the observed count is also much higher than the number that would have been expected.

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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Question

An article included a classification of 91 home runs hit at a certain baseball stadium according to the direction that the ball was hit, resulting in the accompanying data.

Direction	Left Field	Left Center	Center	Right Center	Right Field
Number of Home Runs	17	10	7	19	38

(a)

Let p₁, p₂, p₃, p₄, and p₅ be the proportions of home runs hit in the five directions.

State the appropriate null and alternative hypotheses.

H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 0.2
H_a: H₀ is not true. None of the proportions are equal to 0.2.H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 0.5
H_a: H₀ is not true. At least one of the proportions is not equal to 0.5. H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 0.5
H_a: H₀ is not true. None of the proportions are equal to 0.5.H₀: None of the proportions are equal to 0.5.
H_a: H₀ is not true. p₁ = p₂ = p₃ = p₄ = p₅ = 0.5H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 0.2
H_a: H₀ is not true. At least one of the proportions is not equal to 0.2.

Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.)

X²=P-value=

State the conclusion in the problem context.

Reject H₀. There is convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions.Reject H₀. There is not convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions. Do not reject H₀. There is not convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions.Do not reject H₀. There is convincing evidence to conclude that the proportions of home runs hit are not the same for all five directions.

(b)

Describe how the observed counts for the five directions differ from what would have been expected if the proportions of home runs were the same for all five directions.

For home runs going to left center and center field, the observed counts are significantly higher than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field, the observed count is much lower than the number that would have been expected.For home runs going to left center and center field, the observed counts are significantly lower than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field, the observed count is much higher than the number that would have been expected. For home runs going to left center and center field, the observed counts are significantly lower than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field the observed count is also much lower than the number that would have been expected.For home runs going to left center and center field, the observed counts are significantly higher than the numbers that would have been expected if the proportions of home runs hit were the same for all five directions, while for right field, the observed count is also much higher than the number that would have been expected.

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