Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 423 gram setting. It is believed that the machine is overfilling the bags. A 49 bag sample had a mean of 427 grams. Assume the population standard deviation is known to be 23. Is there sufficient evidence at the 0.05 level that the bags are overfilled?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6:Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

1)

H0: = 423

Ha: > 423

2)

Test statistics

z = - / ​​​​​​/ sqrt(n)

= 427 - 423 / 23 / sqrt(49)

= 1.22

3)

This is one tailed test.

4)

p-value = P( Z > z )

= P( Z > 1.22)

= 0.1112

5)

Level of significance = 0.05

6)

Since test statistics z > 0.05, we do not have sufficient evidence to reject H0.

We conclude that we fail to reject the null hypothesis.