Question 1044974: In a random sample of 23 people, the mean commute time to work was 34.4 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t-distribution to construct a 98% confidence interval for the population mean. What is the margin of error?
The confidence interval for the population mean is?
The margin of error is?
Interpret the results. What do the data say about the sample set?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 98% CI is mean +/- t(0.99, df=22)s/sqrt(n)
34.4+/- 2.508*7.1/sqrt(23); the second part equals 3.7
(30.7,38.1) is the 98% CI.
The margin of error is +/-3.7
It says statistically that the true mean of the population is somewhere between 30.7 and 38.1 with high confidence. We don't know exactly where it is, but we are very confident the interval contains it. The non-statistical interpretation is that the commute time is fairly predictable given that margin of error.
Note, there is not a probability statement here. The true mean, the parameter, either is or isn't in the interval. That isn't a probabilistic statement. Nor is there a confidence interval for the sample. We are completely confident in the sample itself.
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