In testing H0: µ = 3 versus Ha: µ ¹ 3 when =3.5, s = 2.5, and n = 100, what is the p-value?
a.0.0700
b.0.0228
c.0.0655
d.0.0456
For the given test scenario, we have
H0: µ = 3 versus Ha: µ ≠ 3
This is two tailed test.
Test statistic = Z = (Xbar - µ)/[S/sqrt(n)] = (3.5 – 3)/[2.5/sqrt(100)] = .5/.25 = 2
So, P-value = 0.0456
(by using z-table)
Answer: d.0.0456
[Note: P-value for one tailed test = 0.0456/2 = 0.0228]
In testing H0: µ = 100 versus Ha: µ ╪ 100 versus using a sample size of 325, the value of the test statistic was found to be 2.16. The p-value (observed level of significance) is best approximated by 0.0154 0.9692 0.4846 0.0308 0.007
Suppose that ơ is known, for testing H0: µ=µ0 versus alternative of Ha: µ>µ0 (Given µa>µ0), derive a formula to find the value of sample size n, for specified α and β.
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We test the null hypothesis H0: μ = 10 and the alternative Ha: μ ≠ 10 for a Normal population with σ = 4. A random sample of 16 observations is drawn from the population and we find the sample mean of these observations is = 12. The P-value is CLOSEST to: A. 0.9772. B. 0.0456. C. 0.0228. D. 0.6170.
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