Question

A soup company fills cans of soup with ?=10.5 oz, and ?=1.2 oz. A random sample of 31 cans from the production line are weighed and found to have an average weight of 10.1 oz. With ?=0.05, is there evidence to support the claim that the average weight differs from 10.5 oz?

Answer 1

Answer:

Given,

x = 10.1

standard deviation = 1.2

sample n = 31

mean = 10.5

significance level = 0.05

Null hypothesis Ho : u = 10.5

Alternative hypothesis Ha : u != 10.5

consider,

test statistic z = (x - u)/(s/sqrt(n))

substitute values

= (10.1 - 10.5)/(1.2/sqrt(31))

z = - 1.86

Here it is a two tailed test

P value = 2*P(z < - 1.86)

= 0.0628855 [since from z table]

= 0.0629

Here observe that, p value > 0.05 so we fail to reject Ho. So there no sufficient evidence.