SOLVED_ Use the P-value method to test the given hypothesis
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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: $\boxed{\text{There's not su±cient
evidence to support the claim that the mean is lower than 1.7 pounds}}$.
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