We appreciate your visit to A test of the breaking strengths of 6 ropes manufactured by a company showed a sample mean breaking strength of 7750 lbs and a sample. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We have sufficient evidence to support the claim that the true mean breaking strength is not equal to 8000 lbs at a significance level of 0.05.
To determine if we can support the manufacturer's claim of a true mean breaking strength of 8000 lbs, perform a hypothesis test.
Hypotheses:
Null hypothesis (H0): The true mean breaking strength is 8000 lbs.
Alternative hypothesis (Ha): The true mean breaking strength is not equal to 8000 lbs.
Use a two-tailed test with a significance level of 0.05.
This means that if the calculated p-value is less than 0.05, we'll reject the null hypothesis in favor of the alternative hypothesis.
Given:
Sample mean (x) = 7750 lbs
Sample standard deviation (s) = 145 lbs
Sample size (n) = 6
Claimed true mean (μ) = 8000 lbs
Significance level (α) = 0.05
To perform the hypothesis test, calculate the test statistic using the t-distribution:
t = (x - μ) / (s / √n)
t = (7750 - 8000) / (145 / √6)
t ≈ -2.585.
Next, determine the critical value(s) for a two-tailed test with a significance level of 0.05 and degrees of freedom (df) equal to n - 1.
df = 6 - 1 = 5
Using a t-table or a statistical software, the critical values for a two-tailed test with a significance level of 0.05 and 5 degrees of freedom are approximately -2.571 (lower critical value) and 2.571 (upper critical value).
Since the absolute value of our calculated t-value (-2.585) is greater than the critical value of 2.571, we can reject the null hypothesis.
Therefore, we have sufficient evidence to support the claim that the true mean breaking strength is not equal to 8000 lbs at a significance level of 0.05.
Thanks for taking the time to read A test of the breaking strengths of 6 ropes manufactured by a company showed a sample mean breaking strength of 7750 lbs and a sample. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
