Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 424

gram setting. It is believed that the machine is underfilling the bags. A 43 bag sample had a mean of 422 grams. Assume the population variance is known to be 256. 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

Let denotes the true population mean.

To test against

Here

sample mean

population variance

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 0.05 level of significance if P-value < 0.05

Now,

The value of the test statistic

P-value