On Monday night, a pizza company asks a random sample of individuals which topping they like the best on pizza: pepperoni, cheese, or veggies. The results are 74 prefer pepperoni, 40 prefer cheese, and 25 prefer veggies. Distributions Topping FrequenciesLevel CountProbCheese400.28777Pepperoni740.53237Veggie250.17986Total1391.00000N Missing03LevelsTest ProbabilitiesLevel Estim ProbHypoth ProbCheese0.287770.25000Pepperoni0.532370.50000Veggie0.179860.25000TestChiSquareDFProb>ChisqLikelihood Ratio4.076120.1303Pearson3.820120.1481 Method:Fix hypothesized values, rescale omitted (a)On the previous Monday, for the population of all customers, 50% of people preferred pepperoni, 25% preferred cheese, and 25% preferred veggies. They are interested in seeing if this Monday had significantly different proportions than the previous Monday. What is the hypothesis test to be done?H0: p1 = 0.5, p2 = 0.5, p3 = 0.5H1: p1 = p2 = p3H0: ?1 = ?2 = ?3H1: ?1 > ?2 > ?3 H0: ?1 > ?2 > ?3H1: ?1 ≠ ?2 ≠ ?3H0: p1 = 0.5, p2 = 0.25, p3 = 0.25H1: The proportions are not all equal to their hypothesized values.(b)For a 90% confidence level, find the test statistic, critical value, and p-value for the test to be done. (Use the Pearson Chi-Square Goodness of Fit test. Round your test statistic and p-value to four decimal places. Round your critical value to two decimal places.)test statisticcritical valuep-value(c)State the conclusion to the hypothesis test.The null hypothesis should . The proportions on Monday statistically different than the from the previous Monday.(d)To the nearest whole number, what is the largest confidence level where the null hypothesis would be rejected? %You may need to use the appropriate table in the Appendix of Tables to answer this question.

The three categories are cheese, pepperoni, and veggies. The output of the Chi-square test is given.…

Answered: On the previous Monday, for the…

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

On Monday night, a pizza company asks a random sample of individuals which topping they like the best on pizza: pepperoni, cheese, or veggies. The results are 74 prefer pepperoni, 40 prefer cheese, and 25 prefer veggies.

Distributions

Topping

Frequencies

Level	Count	Prob
Cheese	40	0.28777
Pepperoni	74	0.53237
Veggie	25	0.17986
Total	139	1.00000

N Missing

Levels

Test Probabilities

Level	Estim Prob	Hypoth Prob
Cheese	0.28777	0.25000
Pepperoni	0.53237	0.50000
Veggie	0.17986	0.25000

Test	ChiSquare	DF	Prob>Chisq
Likelihood Ratio	4.0761	2	0.1303
Pearson	3.8201	2	0.1481

Method:

Fix hypothesized values, rescale omitted

(a)

On the previous Monday, for the population of all customers, 50% of people preferred pepperoni, 25% preferred cheese, and 25% preferred veggies. They are interested in seeing if this Monday had significantly different proportions than the previous Monday. What is the hypothesis test to be done?

H₀: p₁ = 0.5, p₂ = 0.5, p₃ = 0.5
H₁: p₁ = p₂ = p₃H₀: ?₁ = ?₂ = ?₃
H₁: ?₁ > ?₂ > ?₃ H₀: ?₁ > ?₂ > ?₃
H₁: ?₁ ≠ ?₂ ≠ ?₃H₀: p₁ = 0.5, p₂ = 0.25, p₃ = 0.25
H₁: The proportions are not all equal to their hypothesized values.
(b)

For a 90% confidence level, find the test statistic, critical value, and p-value for the test to be done. (Use the Pearson Chi-Square Goodness of Fit test. Round your test statistic and p-value to four decimal places. Round your critical value to two decimal places.)

test statisticcritical valuep-value
(c)

State the conclusion to the hypothesis test.

The null hypothesis should . The proportions on Monday statistically different than the from the previous Monday.
(d)

To the nearest whole number, what is the largest confidence level where the null hypothesis would be rejected?

%