Stats 200 please help with these 3 questions!! I’ve answered what I could! 15. You take a sample of 22 from…
15. You take a sample of 22 from a population of test scores, and the mean of your sample is 60. (a) You know the standard deviation of the population is 10. What is the 99% confidence interval on the population mean?
We have given that n = 22, sample mean =60 and σ = 10 The 99% C.I. for the population mean is, = sample mean ± 2.58 *σ /√n = 60 ± 2.58 * 10 / √22 = 60 ± 5.501 So, (54.499, 65.501)
(b) Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. What is the 99% confidence interval on the mean now?
18. You were interested in how long the average psychology major at your college studies per night, so you asked 10 psychology majors to tell you the amount they study. They told you the following times: 2, 1.5, 3, 2, 3.5, 1, 0.5, 3, 2, 4. (a) Find the 95% confidence interval on the population mean. (b) Find the 90% confidence interval on the population mean.
106. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours.
a.
i. x ¯ = ____8______
ii. sx = ____4______
iii. n = _____81_____
iv. n – 1 = ___80____
b. Define the random variables X and X ¯ in words.
c. Which distribution should you use for this problem? Explain your choice.
d. Construct a 95% confidence interval for the population mean time wasted.
i. State the confidence interval. CI: (7.12, 8.88)
ii. Sketch the graph.
iii. Calculate the error bound. EB = 0.88
e. Explain in a complete sentence what the confidence interval means.
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