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Suppose that we consider (again) the population of IQ scores of all adults 18 years or older in the United States, but suppose we DO NOT KNOW the population mean, μ, nor are we told the population standard deviation. Suppose we take a sample of 36 adults and it turns out that the sample mean of their IQ scores xbar = 104, and the sample and standard deviation s = 9.
(a). Compute a 95% confidence interval for the true (but unknown) population mean, μ. (Hint: Since we are NOT told the population standard deviation, you will need to use the t-distribution).
(b). Write down in words what this confidence interval represents. Does this mean that there is a 95% probability that the true (but unknown) population mean is in this interval?
(c). Yes or No: If someone was to take ANOTHER sample of 36 adults, and compute a 95% confidence interval for the true (but unknown) population mean, would the interval be the same as the interval in part (a)? Why?
Verified Expert
This file is about finding confidence interval from known sample mean but unknown population mean. for less values of sample t distribution table is more effective. For larger values it becomes closer to normal distribution table. This is a case of interference statistics. by a x% confidence interval means that there is x% probbility that population mean will lie in that interval. greater the confidence interval more is the chances of mean lying in that region. Statistics is an applied branch of maths used to make future prediction with certain level of confidence with known data.
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