The life in hours of a thermocouple used in a furnace is known to be approximate
ID: 3205806 • Letter: T
Question
The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with standard deviation = 20 hours. A random sample of 15 thermocouples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529. We wanted to be 95% confident that the error in estimating the mean life is less than 5 hours. What sample size should we use? Round your asnwer up to the nearest whole number. The answer must be exact.The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with standard deviation = 20 hours. A random sample of 15 thermocouples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529. We wanted to be 95% confident that the error in estimating the mean life is less than 5 hours. What sample size should we use? Round your asnwer up to the nearest whole number. The answer must be exact.
The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with standard deviation = 20 hours. A random sample of 15 thermocouples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529. We wanted to be 95% confident that the error in estimating the mean life is less than 5 hours. What sample size should we use? Round your asnwer up to the nearest whole number. The answer must be exact.
Explanation / Answer
When sample data is collected and the sample mean x is calculated, that sample mean is typically different from the population mean . The margin of error E is the maximum difference between the observed sample mean x and the true value of the population mean . Here the margin of error is 5.
The number of sample size is determined by :
n = [z/2 * / E ]2
z/2 is the critical value, the positive value that is at the vertical boundary for the area of in the right tail of the standard normal distribution.
is the population standard deviation. = 20
n is the sample size
A 95% degree confidence corresponds to = 0.05. The critical value z/2 = 1.96 from z table
n = [1.96*20/5]2 = 61.46 ~ 62 samples
therefore, 62 samples are to be chosen.
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