SOLVED_ Use the P-value method to test the given hypothesis

.pdf

School

University of Colorado, Boulder *

*We aren’t endorsed by this school

Course

140

Subject

Economics

Date

Apr 29, 2024

Type

pdf

Pages

1

Uploaded by DeanPower12340 on coursehero.com

4/11/24, 8:58 PM SOLVED: Use the P-value method to test the given hypothesis. The Maine Department of Natural Resources reported that the mean weight of lo… https://www.numerade.com/ask/question/use-the-p-value-method-to-test-the-given-hypothesis-the-maine-department-of-natural-resources-reported-that-the-mean-we… 1/1 INSTANT ANSWER EXPERT VERIFIED VIDEO ANSWER Step 1/5 State the null and alternative hypotheses. Null hypothesis (H0): The mean weight of lobsters is 1.7 pounds, i.e., μ = 1.7. Alternative hypothesis (H1): The mean weight of lobsters is less than 1.7 pounds, i.e., μ < 1.7. Step 2/5 Determine the level of significance. α = 0.01 Step 3/5 Calculate the test statistic. We will use the t-test statistic since we have a small sample size (n = 38) and the population standard deviation is unknown. t = (x̄ - μ) / (s / √n) t = (1.5 - 1.7) / (0.6 / √38) t ≈ -2.32 Step 4/5 Determine the critical value and the P-value. Using a t-distribution table or calculator, we find the critical value for a one-tailed test with 37 degrees of freedom and α = 0.01 is approximately -2.43. Now, we need to find the P-value associated with our test statistic. Using a t-distribution calculator, we find that the P- value for t = -2.32 and 37 degrees of freedom is approximately 0.0127. Answer Compare the P-value to the level of significance and make a decision. Since the P-value (0.0127) is greater than the level of significance (0.01), we fail to reject the null hypothesis. Therefore, there is not su±cient evidence to support the claim that the mean weight of lobsters is lower than 1.7 pounds. Final answer: $\boxed{\text{There's not su±cient evidence to support the claim that the mean is lower than 1.7 pounds}}$. Want more help with this problem? Live Chat with Ace? Search for answers and textbooks Textbooks Ace - AI Tutor NEW Ask our Educators Study Tools
Discover more documents: Sign up today!
Unlock a world of knowledge! Explore tailored content for a richer learning experience. Here's what you'll get:
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help