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Question: 1 a bearing used in an automotive application is supposed...

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1. A bearing used in an automotive application is supposed to have a nominal inside diameter of 3.81 cm. A random sample of 25 bearings is selected and the average inside diameter of these bearings is 3.8037 cm. Bearing diameter is known to be normally distributed with standard deviation σ 0.03 cm. (a) Compute a 95%-confidence interval for the mean inside diameter. (b) Test the hypothesis H0 : μ = 3.81 versus H1 : μ关3.81 using α-001. What is the P-value for the test? 2. Let X be the length of life of a 60-watt light bulb manufactured by a certain company. If a random sample of 25 units is tested until they burn out, yielding a sample mean of x = 1478 hours and s, 1296, compute a confidence 95 %-confidence interval for the mean and the variance. 3. A manufacturing firm claims that the batteries used in its electronic games will last an average of 30 hours. To maintain this average, 16 batteries are tested each month. If the computed t-value falls between -to.025 and to.025, the firm is satisfied with its claim. What conclusion should the firm draw from a sample that has a mean of 27.5 hours and a standard deviation of s 5 hours? Assume the distribution of battery lives to be approximately normal.
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