Question

Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 78 manufacturing companies located in the Southwest. The mean expense is $49.87 million and the standard deviation is $11.68 million. Is it reasonable to conclude the sample data are from a population that follows a normal probability distribution?

Advertising Expense ($ Million)	Number of Companies
25 up to 35		8
35 up to 45		20
45 up to 55		24
55 up to 65		17
65 up to 75		9
Total		78

1-) State the decision rule. Use the 0.02 significance level. (Round your answer to 2 decimal places.)

H₀: The population of advertising expenses follows a normal distribution.

H₁: The population of advertising expenses does not follow a normal distribution.

Reject Ho if chi-square > ___________

2-) Compute the value of chi-square. (Round your answer to 2 decimal places.)

Chi-square value __________

3-) What is your decision regarding H₀?

__________ Ho . This data _________ from a normal distribution.

Answer 1

1)here k =number of categories =5 ; m =estimated value =2

degree of freedom = k-m-1     =5-2-1 =

2

for 2 degree of freedom and 0.02 level critical value = 7.82

Reject Ho if chi-square > 7.82

2)

observed	Normal	Normal	Expected	χ2=(O-E)2/E
frequency(O)	probabilty	probabilty(p)	frequency(E=p*ΣO)
8	P(X<35)	0.1020	7.96	0.000
20	P(35<X<45)	0.2352	18.35	0.149
24	P(45<X<55)	0.3328	25.96	0.148
17	P(55<X<65)	0.2332	18.19	0.078
9	P(65<X<)	0.0968	7.55	0.278
78		1.0000	78	0.653

Chi-square value =0.65

3)

fail to reject Ho , this data is from a normal distribution.