Question

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 91 hours. A random sample of 49 light bulbs indicated a sample mean life of 340 hours. Complete parts​ (a) through​ (d) below. a. Construct a 99​% confidence interval estimate for the population mean life of light bulbs in this shipment. The 99​% confidence interval estimate is from a lower limit of nothing hours to an upper limit of nothing hours. ​(Round to one decimal place as​ needed.) b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 390 ​hours? Explain. Based on the sample​ data, the manufacturer has the right to state that the lightbulbs have a mean life of 390 hours. A mean of 390 hours is ▼ standard errors ▼ below above the sample​ mean, so it is ▼ likely highly unlikely that the lightbulbs have a mean life of 390 hours. c. Must you assume that the population light bulb life is normally​ distributed? Explain. A. ​Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. B. ​No, since sigma is​ known, the sampling distribution of the mean does not need to be approximately normally distributed. C. ​Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. D. ​No, since sigma is known and the sample size is large​ enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem. d. Suppose the standard deviation changes to 70 hours. What are your answers in​ (a) and​ (b)? The 99​% confidence interval estimate would be from a lower limit of nothing hours to an upper limit of nothing hours. ​(Round to one decimal place as​ needed.) Based on the sample data and a standard deviation of 70 ​hours, the manufacturer ▼ has does not have the right to state that the lightbulbs have a mean life of 390 hours. A mean of 390 hours is ▼ less than 2 5 standard errors ▼ above below the sample​ mean, so it is ▼ highly unlikely likely   that the lightbulbs have a mean life of 390 hours

Answer 1

Based on the sample data and a standard deviation of 70 ​hours, the manufacturer  does not have the right to state that the lightbulbs have a mean life of 390 hours. A mean of 390 hours is 5 standard errors above the sample​ mean, so it is unlikely  that the lightbulbs have a mean life of 390 hours