Question

5. An analysis of the fat content, X % of a random sample of 175 particular burgers resulted in the following table.

Fat Content	No of Burgers
26 ≤ ? ≤ 28	7
28 ≤ ? ≤ 30	22
30 ≤ ? ≤ 32	36
32 ≤ ? ≤ 34	45
34 ≤ ? ≤ 36	33
36 ≤ ? ≤ 38	28
38 ≤ ? ≤ 40	4

Can it be assumed that the fat content of this grade of the burger is normally distributed?

Answer 1

Ho: distribution is normal probability distribution
Ha: distribution is not the normal probability distribution

mean,µ=   33
std dev,s=   2.91

total observation , n =   175

lower bound	upper bound	percentage	observed frequency,O	expected frequency ( E )=5	(O-E)²/E
26.00	28.00	0.0429	7	7.50	0.034
28.00	30.00	0.1084	22	18.97	0.483
30.00	32.00	0.2143	36	37.50	0.060
32.00	34.00	0.2689	45	47.05	0.090
34.00	36.00	0.2143	33	37.50	0.539
36.00	38.00	0.1084	28	18.97	4.297
38.00	40.00	0.04	4	7.50	1.636

chi square test statistic,X² = Σ(O-E)²/E =   7.139

level of significance, α=   0.05              
Degree of freedom=k-3 =    7     -   3   =   4

Critical value =    9.4877   [ Excel function: =chisq.inv.rt(α,df) ]          
decision: Fail to reject Ho

it can be assumed that the fat content of this grade of the burger is normally distributed