SOLUTION: Can some please show me how to use the chi-squared distribution to test the hypothesis of this problem? A restaurant owner wants to see if the business is good enough for him to

Question 1064093: Can some please show me how to use the chi-squared distribution to test the hypothesis of this problem?
A restaurant owner wants to see if the business is good enough for him to purchase a restaurant. He asks the present owner for a breakdown of how many customers that come in for lunch each day and the results are as follows: Monday - 20, Tuesday - 30, Wednesday - 25, Thursday - 40 and Friday - 55. The prospective owner observes the restaurant and finds the following number of customers coming for lunch each day: Monday- 30, Tuesday - 15, Wednesday- 7, Thursday 40, and Friday - 33. At a 95% confidence level determine whether the present owner reported the correct number of customers for lunch each day.

Thank you in advance
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
restaurant owner's sample is 20+30+25+40+55 = 170
p1 = 20/170 = 0.12 for Monday
p2 = 30/170 = 0.18 for Tuesday
p3 = 25/170 = 0.15 for Wednesday
p4 = 40/170 = 0.23 for Thursday
p5 = 55/170 = 0.32 for Friday
:
prospective owner's sample is 30+15+7+40+33 = 125
:
H0: The distribution of the prospective owners sample is 0.12, 0.18, 0.15, 0.23, 0.32
:
H1: H0 is false
:
strictly speaking in order to use chi-squared distribution we must check for
:
min(0.12(125) +0.18(125), 0.15(125), 0.23(125), 0.32(125)) > 5
:
min(15, 22, 19, 29, 40) > 5, yes since 15 > 5
:
degrees of freedom = 5 - 1 = 4 and a 95% confidence level
:
the X^2 table for 4 degrees of freedom and a = 0.05 ( 1 - 95/100)
:
the critical value is 9.49
:
we reject H0 if X^2 > or = 9.49
:
X^2 = summation from 1 to 5 ( observed value - expected value)^2 / expected value
:
Note the expected values are (15, 22, 19, 29, 40) and observed values are (30, 15, 7, 40, 33)
:
X^2 = 30.02
:
***********************************************************************
we reject H0 - the owner did not report the correct number of customers
***********************************************************************
:

RELATED QUESTIONS
Prof. Green�s multiple-choice exam had 50 questions with the distribution of correct... (answered by stanbon)

Please help me in answering this question. In a standard normal distribution, what is the (answered by stanbon)

Please help me solve these problems. 1. Calculate the sample mean and standard... (answered by stanbon)

Stan, please explain the characteristics of a Chi-Square Goodness of Fit hypothesis test... (answered by stanbon)

Please help me. I am lost with this question. Thank you for your help In a 3-digit... (answered by stanbon)

Please help me. I am not understanding this question. In a 3-digit lottery, each of... (answered by stanbon)

Hi, I am having problems with a chi-square related question. Here is the question: (answered by stanbon)

Suppose you conduct research to test student preference among five types of candy. One... (answered by stanbon)

Could you PLEASE SHOW me how to solve problem? Provide an appropriate response. A... (answered by Theo)