Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 419 gram setting. It is believed that the machine is underfilling the bags. A 19 bag sample had a mean of 412 grams with a variance of 784. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled

Answer 1

Answer:

The calculated t- value = 1.09 > 3.19 at 0.025 level of significance

Null hypothesis is rejected

There is sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

Step(i):-

Given the mean of the Population(μ)  = 419 grams

The sample size 'n' =19

Given mean of the sample x⁻ = 412

Given variance of the sample S² = 784

                                                 S = √784 = 28

Step(ii):-

Null hypothesis: H₀: There is no sufficient evidence to support the claim that the bags are underfilled.

Alternative hypothesis: H₁:

There is sufficient evidence to support the claim that the bags are underfilled.

Test statistic

                     $t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }$

                    $t = \frac{412 -419}{\frac{28}{\sqrt{19} } }$

                   t = -1.09

                 |t| = |-1.09|

Degrees of freedom   ν = n-1 = 19-1 =18

t₀.₀₂₅ =  3.19

Final answer:-

The calculated t- value = 1.09 > 3.19 at 0.025 level of significance

Null hypothesis is rejected

There is sufficient evidence to support the claim that the bags are underfilled