Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 412 gram setting. It is believed that the machine is underfilling the bags. A 28 bag sample had a mean of 404 grams with a standard deviation of 29. Assume the population is normally distributed. 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 given sample mean = 404

SD = 29

Z-score = (X - ) / SD

Here X = 412 because that is the value at which we want to whether the bag filling machine works

So z-score = (412 - 404) / 29

= 8/29

= 0.275862

Here we should use a two-tailed test becuase we are just checking whether the bag filling machine works correctly at 412 gram setting or not

The p-value for a z-score of 0.278562 for a two tailed test is at 0.05 level of significance is 0.1957 which can be calculated online from p-value calculators

So the p-value is 0.1957 rounded to four decimal places