A pizza lover wants to compare the average delivery times for four local pizza r

Question

A pizza lover wants to compare the average delivery times for four local pizza restaurants. Over the course of a few weeks, he orders a number of pizzas from cach restaurant, and he records the time it takes for each pizza to be delivered. a) When performing an ANOVA with this data, what is the altemative hypothesis? All of the restaurants have different mean delivery times Two of the restaurants have different mean delivery times O One of the restaurants has a different mean delivery time than the others At lcast two of the restaurants have different mcan delivery times b) A partial ANOVA table for his data is shown below. What is the value of ? 16.56 2045.451 otal c) what is the value of C·n the ANOVA table? d) What is the value of D in the ANOVA table? Give your answer to three decimal places e) What is the value of E in the ANOVA table? Give your answer to three decimal places. f) what is the value of F in the ANOVA table? Give your answer to two decimal places g) What is the value of in the ANOVA table? Give your answer to four decimal places. h) Using a 0.05 level of significance, what should his conclusion be in this case? He should conclude that at least two of the restaurants have different mean delivery times because the P-value is greater than 0.05 He should conlude that at all of the restaurants have the same mean delivery times because the P-value is less than 0.05. He should fail to reject the claim that at all of the restaurants have the same mean delivery times because the P-value is greater than 0.05 He should conclude that at least two of the restaurants have different mean delivery times because the P-value is less than 0.05.

Explanation / Answer

Ans:

a)At least two of the restaurants have different mean delivery times.

(last option is correct)

b)df(treatments)=4-1=3

c)df(error)=20-3=17

d)MS(treatments)=28.891/3=9.630

e)MS(error)=16.56/17=0.974

f)F=9.630/0.974=9.89

g)p-value=Fdist(9.89,3,17)=0.0005

h)As,p-value<0.05,we reject null hypothesis.

he should conclude that at least two of the restaurants have different mean delivery times because the p-value is less than 0.05.

(last option is correct)

DF SS MS F p-value Treatments 3 28.891 9.630 9.89 0.0005 Error 17 16.56 0.974 Total 20 45.451

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