Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 420 gram setting. It is believed that the machine is underfilling the bags. A 43 bag sample had a mean of 415 grams. Assume the population standard deviation is known to be 20. A level of significance of 0.01 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

Since it says it is beleived that the machine is underfilling the bags, we use a 1 tailed left tailed test.

Given: = 420 gms, = 20 gms, = 415 gms, n = 43, = 0.01

The Hypothesis:

H0: = 420 gms

Ha: < 420 gms

This is a Left Tailed Test.

The Test Statistic: Since the population standard deviation is known, we use the students z test.

The test statistic is given by the equation:

The p Value:    The p value for Z = -1.64 from the normal distribution tables: p value = 0.0505

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The Decision Rule:   If P value is < , Then Reject H0.

The Decision:   Since P value (0.0505) is > (0.01) , We Fail to Reject H0.

The Conclusion: There is insufficient evidence at the 99% significance level to conclude that the mean population weight of the bags being filled by the machine is less than 420 gms.