Question

.6 The expected mean of a normal population is 100, and its standard deviation is 12. A sample of 49 measurements gives a sample mean of 96. Using the α = 0.01 level of significance a test is to be made to decide between “population mean is 100” or “population mean is different than 100.” a) State null H0. b) What conclusion can be drawn at the given level of significance α = 0.01. c) What conclusion can be drawn if α = 0.05? d) What is the p-value of the test? e) State the type I and II errors. f) What is probability of type II error when, if mean μ really is 102 and α = 0.05 ? [5+5+5+5+5+5 = 30]

Answer 1

From the given information,

By using calculator,

The required correct answers are,

a) Null hypothesis (Ho): μ = 100

b) failed to reject null hypothesis.

Conclude that mean is 100.

c) Reject the null hypothesis.

Conclude that mean is not equal to 100.

d) p-value= 0.01964

e) Type I error means that give conclusion mean is not equal to 100 when it is actually equal to 100 and type II error is that give conclusion as mean is equal to 100 when it not equal to 100 in fact.

f) By using calculator,

Probability of type II error is 0.0025

Thank you.