Question

The following data were selected randomly from a normally distributed population of values represent the percent of fat in a certain type of steak burger. The manufacturer claims that the mean fat percent is less than 20%. Use 10% level of significance and population variance 9 to test the manufacturer claim.

21, 18, 19, 16, 18, 24, 22, 19, 24, 14, 18, 15.

Answer 1

∑x = 228

n = 12

Mean , x̅ = Ʃx/n = 228/12 = 19

σ² = 9

So, σ = 3

Null and Alternative hypothesis:

Ho : µ = 20

H1 : µ < 20

Critical value, z crit = NORM.S.INV(0.1) = -1.282

Reject Ho if z < -1.282

Test statistic:

z = (x̅- µ)/(σ/√n) = (19 - 20)/(3/√12) = -1.1547

p-value :

p-value = NORM.S.DIST(-1.1547, 1) = 0.1241

Decision:

p-value > α, Do not reject the null hypothesis

Conclusion:

There is not enough evidence to conclude that the mean fat percent is less than 20% at 10% level of significance.