Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 413.0 gram setting. Based on a 46 bag sample where the mean is 420.0 grams, is there sufficient evidence at the 0.05 level that the bags are overfilled? Assume the standard deviation is known to be 17.0.

Step 1 of 5: Enter the hypotheses:

Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places.

Step 3 of 5: Specify if the test is one-tailed or two-tailed.

Step 4 of 5: Enter the decision rule.

Step 5 of 5: Enter the conclusion.

Answer 1

Given that, sample size ( n ) = 46

sample mean ( M ) = 420.0 grams

population standard deviation = 17.0

significance level = 0.05

Step 1) The null and the alternative hypotheses are,

Step 2) Test statistic is,

Step 3) This test ia one-tailed ( right-tailed)

Step 4) critical value at 0.05 level is, Z^* = 1.645

Decision Rule: Reject H₀, if test statiatic > 1.645

Step 5) Since, test statistic = 2.79 > 1.645

We reject the null hypothesis ( H₀ ).

Conclusion: There is sufficient evidence at the 0.05 level that the bags are overfilled.