Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 447 gram setting. It is believed that the machine is underfilling the bags. A 39 bag sample had a mean of 441 grams. Assume the population standard deviation is known to be 24. A level of significance of 0.05 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: the machine is not under filling the bags.

Alternative hypothesis: Ha: the machine is under filling the bags.

H0: µ = 447 versus Ha: µ < 447

This is a lower tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 447

Xbar = 441

σ = 24

n = 39

α = 0.05

Critical value = -1.6449

(by using z-table or excel)

Z = (441 – 447)/[24/sqrt(39)]

Z = -1.5612

P-value = 0.0592

(by using Z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the machine is under filling the bags.