A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 46 cables and apply weights to each of them until they break. The 46 cables have a mean breaking weight of 779.2 lb. The standard deviation of the breaking weight for the sample is 15.3 lb. Find the 90% confidence interval to estimate the mean breaking weight for this type cable. Your answer should be rounded to 2 decimal places.
Added by Silvia M.
Step 1
Given that we want a 90% confidence interval, we need to find the critical value for a t-distribution with 45 degrees of freedom. Using a t-table or software, the critical value is approximately 1.679. Show more…
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A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 40 cables and apply weights to each of them until they break. The 40 cables have a mean breaking weight of 775.3 lb. The standard deviation of the breaking weight for the sample is 14.9 lb. Find the 90% confidence interval to estimate the mean breaking weight for this type cable. ( , ) Your answer should be rounded to 2 decimal places.
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A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 42 cables and apply weights to each of them until they break. The 42 cables have a mean breaking weight of 778.9 lb. The standard deviation of the breaking weight for the sample is 15.1 lb. Find the 95% confidence interval to estimate the mean breaking weight for this type cable. ( ), () Your answer should be to 2 decimal places.
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