Question

A can of soda is labeled as containing 13 fluid ounces. The quality control manager wants to verify that the filling machine is not over dash fillingnot over-filling

the cans. Complete parts​ (a) through​ (d) below.

​(a) Determine the null and alternative hypotheses that would be used to determine if the filling machine is calibrated correctly.

b) The quality control manager obtains a sample of 75 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test.

There______________sufficient evidence to conclude that the machine is out of calibration.

(c)​ Suppose, in​ fact, the machine is not out of calibration. Has a Type I or Type II error been​ made?

A ___________has been made since the sample evidence led the​ quality-control manager to__________the null​ hypothesis, when the _______is true.

(d) Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration.

What level of significance would you recommend the quality control manager to​ use? Explain.

The level of significance should be _____________because this makes the probability of Type I error ___________.

Answer 1

a.)

Null Hypotheses, Ho: Machine is calibrated correctly

Alternate Hypothese, Ha: Machine is not calibrated correctly

b.)

Since Manager rejects the Null Hypotheses.

There is sufficient evidence to conclude that machine is out of calibration

c.)

-> A Type 1 has been made

-> to Reject Null Hypotheses, when Null Hypotheses is true

d.)

Since management wants the evidence to be overhelming that machine is out of calibration.

Level of significance: 1%

Probability of type 1 error = 0.01