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STA 100 Quiz 2- Take Home Part Due First Class After Exam Prof. Thistleton
Suppose that you have been told that the mean Life Orientation Test score for a certain population is μ 0 = 16. You wish to test this and so obtain a simple random sample and produce the following data (test scores): xi x^2 i 15 18 17 17 12 13
- Calculate the sample mean, x and sample standard deviation, s.
- Calculate the 90% confidence interval for the population mean (by hand).
- Test at the α = 0.05 level of significance whether the population mean is really μ = 16 (by hand).
- Calculate the 90% confidence interval for the population mean using SPSS.
- Test at the α = 0.05 level of significance whether the population mean is really μ = 16 using SPSS.
STA 100 Quiz 2 November 15, 2006 Prof. Thistleton
- Let Z be standard normal, i.e. let Z have a normal distribution with mean μ = 0 and standard deviation σ = 1, Z ∼ N (0, 1).
(a) Calculate P (Z < 1 .43)
(b) Calculate P (Z > 2 .03)
(c) Calculate P (− 1. 15 < Z < 1 .69).
- Suppose a population is distributed normally with mean μ = 10 and standard deviation σ = 2, that is X ∼ N (10, 22 ).
(a) Calculate P (X < 8 .2)
(b) Calculate P (X > 10 .1)
(c) Calculate P (7. 5 < X < 11).
- A population of test scores is normally distributed with a mean of 100 and a standard deviation of 10.
(a) Calculate the probability that a randomly selected individual from this population will have a score x greater than 105 points. (Be sure to use the continuity correction).
(b) Calculate the probability that a randomly selected sample of size n = 40 from this population will have a mean score ¯x greater than 105 points.
(c) Calculate the probability that a randomly selected sample of size n = 100 from this population will have a mean score ¯x greater than 105 points.
(d) What score does someone need to obtain to be in the top 10% of the population?
- Form a 95% confidence interval for a population proportion, p, if you sample and obtain r = 120 from a sample of size n = 300.
- A population is normally distributed. You form a simple random sample of size 23 from this population and obtain a sample standard deviation of 15 and a sample mean of 103.
(a) Form a 99% confidence interval for the population mean based upon your sample data.
(b) Form a 99% confidence interval for the population mean if you know σ = 15.
(c) Using your sample data (i.e. using the sample standard deviation) test at the α = 0. 05 level of significance whether the population mean is 95 against the alternative that is is lower.
(d) Repeat your test if you use the population standard deviation given above, σ = 15.
