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Introduction to Confidence Intervals (page 248)
In chapter 7 we discussed how to make inferences about a population parameter based on a sample statistic. While this can be useful, it has severe limitations. In Chapter 8, we expand our toolbox to include Confidence Intervals. Instead of basing our inference on a single value, a point estimate, a Confidence Interval provides a range of values, an interval, which – at a certain level of confidence (90%, 95%, etc.) – contains the true population parameter. Having a range of values to make inferences about the population provides much more room for accuracy than making an inference off of only one value.
When we worked with probabilities based on sample means, we learned that there is …show more content…

Assume that the population standard deviation is fairly stable at 1.8 hours.
Calculate the 95% confidence interval for the population mean weekday sleep time of all adult residents of this Midwestern town.
95% = 1.96 6.4 +(-) 1.96 x (1.8/sqrt80) = [6.01, 6.79]
Can we conclude with 95% confidence that the mean sleep time of all adult residents in this Midwestern town is not 7 hours?
Yes, we can conclude with 95% confidence that the mean sleep in this Midwestern town is not 7 hours because the value 7 does not fall within the confidence interval.
Confidence Interval for the Population Mean when Sigma is Unknown
While it is possible that we could know enough about our population to make an assumption about what the population standard deviation is, it is much more likely that if we do not know the population mean, then we do not know the population standard deviation. In this case, we can’t use the standard normal distribution, and we use a different distribution, the Student’s t distribution. Instead of , we use s, the sample standard deviation.
The formula is: x±ta/2, df sn .
/2 is still defined the same way, and df is degrees of freedom, calculated as n-1, where n is the sample size. Degrees of freedom determine the extent of the broadness of the tails of the distribution; the fewer the degrees of freedom, the broader the tails.
Solve the following problems:
Find ta/2, df for the following confidence levels: T-SCORE

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