A reporter with India Paper is working on a story about the main factors making
ID: 3306097 • Letter: A
Question
A reporter with India Paper is working on a story about the main factors making restaurants in the St. Pete area different from each other. The variable he is considering is the average meal price per person. The reporter selects a sample of 5 restaurants serving Italian food, Seafood and Steaks. The reporter believes that average price meal per person in the St Pete area is about the same independently of the type of restaurant. The table below shows sample mean and variances for collected data in dollars. Allow for an alpha of 0.05.
Italian Seafood Steakhouse
Sample Mean 14 17 20
Sample Variance 2.5 2.5 16
a. How many degrees of freedom are there in the problem?
b. what's the critical value
c. What is the value for the mean of the means?
d. What is the value of SSTR and MSTR respectively?
e. What is the value of SSE and MSE respectively?
f. What is the value for the test statistic?
g. What is your decision after performing the test?
h. What is your conclusion after the test?
Explanation / Answer
from above data:
a) degree of freedom -=5*3-1 =14
b)critical value=3.8853
c)mean of the means=17
d)SSTR =90 ; MSTR=45
e)SSE =84 ; MSE =7
f) test stat F =6.429
g) as test stat is higher then critical value we reject null hypothesis
h) there is evidence that average price meal per person in the St Pete area is different independentlyat least between two types of restaurant.
i ni Xi Si^2 ni*(Xi- grand mean)^2 (ni-1)*Si^2 Italian 5 14 2.500 45.000 10.000 seafood 5 17 2.500 0.000 10.000 Steakhouse 5 20 16.000 45.000 64.000 Weighted mean 17.000 90.000 84.000 SSG SSE Source of variation SS df MS F P value F crit treatment 90.000 2 45.000 6.429 0.0127 3.8853 error 84.000 12 7.000 total 174.000 14Related Questions
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