Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly...

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 409 gram setting. It is believed that the machine is underfilling the bags. A 20 bag sample had a mean of 399 grams with a standard deviation of 21. Assume the population is normally distributed. A level of significance of 0.02 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.

Hypotheses are,

H0: $\mu$ = 409 grams

H1:  $\mu$ < 409 grams

Given,

Sample mean $\bar{x}$ = 399 grams

Sample standard deviation, s = 21

Hypothesized mean, $\mu$ = 409 grams

Since we do not know the population standard deviation, we will use t test statistic.

Standard error of mean = s / $\sqrt{n}$ = 21 / $\sqrt{20}$ = 4.696

t = (399 - 409) / 4.696 = -2.13

Degree of freedom = n - 1 = 20 - 1 = 19

For left tail test, p-value = P(t < -2.13, df = 19) = 0.0232

Since, p-value is greater than 0.02 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that the machine is underfilling the bags.

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