A manufacturer of detergent claims that the contents of boxes sold weight on average of 16 ounces. The distribution of weight is known to be normal, with a standard deviation of 0.4 ounce. A random sample of 16 boxes yielded a sample mean weight of 15.84 ounces. (a) Determine null and alternative hypothesis. (b) Calculate the test statistics and P-value. (c) Determine the conclusion at a 10% significance level.
Added by John P.
Close
Step 1
Step 1: The null hypothesis is that the average weight of the boxes is 16 ounces (H0: μ = 16), and the alternative hypothesis is that the average weight is not 16 ounces (Ha: μ ≠ 16). Show more…
Show all steps
Your feedback will help us improve your experience
Rosina Dapaah and 77 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A manufacturer of detergent claims that the contents of boxes sold weigh on average at least 30 ounces. The distribution of weights is known to be normal, with a standard deviation of 0.77. A random sample of 25 boxes yielded an average weight of 30.19 ounces. Suppose an inspector wants to test the null hypothesis that the population mean weight is at least 30 ounces. That is, test the null hypothesis H0: μ = 30 against the alternative hypothesis H1: μ < 30. Answer the following, rounding off your answers to two decimal places. (a) What is the test statistic used in the decision rule? (b) What is the critical value the inspector will use? Use a 10% level of significance.
Thuc N.
A manufacturer of detergent claims that the contents of boxes sold weigh on average at least 30 ounces. The distribution of weights is known to be normal, with standard deviation 0.78. A random sample of 20 boxes yielded an average weight of 29.92 ounces. Suppose an inspector wants to test the null hypothesis that the population mean weight is at least 30 ounces. That is, test the null hypothesis H0 : μ = 30 against the alternative hypothesis H1 : μ < 30 Answer the following, rounding off your answers to two decimal places. (a) What is the test statistic used in the decision rule? (b) What is the critical value the inspector will use? Use a 10% level of significance. (c) What decision do you make? A. Do not reject the null hypothesis. B. Reject the null hypothesis.
Madhur L.
Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Coffee Vending Machines The Brazil vending machine dispenses coffee, and a random sample of 27 filled cups have contents with a mean of 7.14 oz and a standard deviation of 0.17 oz. Use a 0.05 significance level to test the claim that the machine dispenses amounts with a standard deviation greater than the standard deviation of 0.15 oz specified in the machine design.
Hypothesis Testing
Testing a Claim About a Standard Deviation or Variance
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD