Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 408.0 gram setting. It is believed that the machine is underfilling the bags. A 45 bag sample had a mean of 406.0 grams. A level of significance of 0.01 will be used. Is there sufficient evidence to support the claim that the bags are underfilled

Answer 1

There is no sufficient evidence to support the claim that the bags are underfilled

Explanation:

Null [H0] : chips x = 408

Alternate [H1] : chips x < 408

t = ( x' - u ) / (s / √n)

x' = sample mean , u = population mean, s = standard deviation, n = no. of observations.

(406 - 408) / (21 /√45)

-2 / 3.13

= 0.64

t value for α = 0.01 (one tailed), with degree of freedom = 44 : is 2.41

As calculated t 0.64 < tabulated t 2.41. So we don't reject the null hypothesis & state that chips x = 408