Question

1. A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Based on a 19 bag sample where the mean is 451 grams and the standard deviation is 21, is there sufficient evidence at the 0.025 level that the bags are overfilled? Assume the population distribution is approximately normal.

-State the null and alternative hypotheses.

-Find the value of the test statistic. Round your answer to three decimal places.

-Specify if the test is one-tailed or two-tailed.

-Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

-Make the decision to reject or fail to reject the null hypothesis.

2. The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.02 level that the drug stays in the system for more than 378 minutes. For a sample of 84 patients, the mean time the drug stayed in the system was 385 minutes. Assume the standard deviation is known to be 24.

-Enter the hypotheses:

-Enter the value of the z test statistic. Round your answer to two decimal places.

-Specify if the test is one-tailed or two-tailed.

-Enter the decision rule.

-Enter the conclusion.

3.The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.05 level that the medicine relieves pain in less than 373 seconds. For a sample of 42 patients, the mean time in which the medicine relieved pain was 365 seconds. Assume the standard deviation is known to be 18.

State the null and alternative hypotheses for the above scenario.

4.A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.18 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 17 bolts has an average diameter of 0.19⁢cm with a standard deviation of 0.2744. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.025 level?

-State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary.

-Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

-Determine the value of the test statistic. Round your answer to three decimal places.

-Make the decision. (Reject Null Hypothesis or Fall to Reject Null Hypothesis)

-What is the conclusion?

Answer 1