1. Refer to the output from section 2 of the Minitab, where you calculated both
ID: 3055210 • Letter: 1
Question
1. Refer to the output from section 2 of the Minitab, where you calculated both a t- and a s- confidence interval from the data in column el. Verify that each interval is correet by plugging into the formulas for calculating z- and i-confidence intervals. z-interval: -interval If you were working in the 'real world' and in the course of your research came across the data in column cl, which of the above two confidence intervals would you be more likely to calculate? Why? would be more aceurate Now refer to the 50 confidence intervals calculated in part 3, (a) 2. How many of the 90% confidence intervals doweexpect to contain the true population mean 100? Show your work. aspe How manyof the 99% confidence intervals do we expect to contain the true population mean of 100? Show your work. (b) (L,? (c) On y (d) (e) (0 our Minitab output, mark any intervals which do not contain the population mean. How many of the 90% confidence intervals actually contained 100? How many of the 99% confidence intervals actually contained 100? which type of interval (90% confidence or 99% confidence) is wider? Explain. Are 99% confidence intervals better, in general, than 90% confidence intervals? Explain.Explanation / Answer
t interval -
M = 105.61
t = 1.73
sM = ?(15.622/20) = 3.49
? = M ± t(sM)
? = 105.61 ± 1.73*3.49
? = 105.61 ± 6.0394
You can be 90% confident that the population mean (?) falls between 99.5706 and 111.6494.
z test interval
M = 105.61
t = 1.64
sM = ?(152/20) = 3.35
? = M ± Z(sM)
? = 105.61 ± 1.64*3.35
? = 105.61 ± 5.517
You can be 90% confident that the population mean (?) falls between 100.093 and 111.127.
In real world, we does not know the population standard deviation. So it is better to use t test .
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