Question

A sample of size 234, taken from a normally distributed population whose standard deviation is known to be 5.70, has a sample mean of 75.54. Suppose that we have adopted the null hypothesis that the actual population mean is greater than or equal to 76, that is, H₀ is that μ ≥ 76 and we want to test the alternative hypothesis, H₁, that μ < 76, with level of significance α = 0.1.

a)

What type of test would be appropriate in this situation?

	A right-tailed test.
	A left-tailed test.
	A two-tailed test
	None of the above

b) What is the critical value? (for a two-tailed test give the positive value)

answer should be accurate to at least two decimal places.

Critical value: ______

c) What is the computed test statistic?
answer should be accurate to at least two decimal places.

Test statistic: ______

d)

Based on your test statistic and the decision rule you have decided upon, what can we conclude about H₀?

	There is sufficient evidence, at the given significance level, to reject H0.
	There is insufficient evidence, at the given significance level, to reject H0; or we fail to reject H0.
	There is insufficient evidence to make it clear as to whether we should reject or not reject the null hypothesis

Answer 1

n= 234, =5.70, =75.54, =76, =0.10

H0: μ ≥ 76

H1:  μ < 76

a) A left-tailed test.

  b) Critical value for = 0.10 is calculated from Normal Z table, we get,

Critical value = -1.28

c) Calculate test statistics

Z= -1.234499

Test statistic = -1.23

  d) Decision rule:

Reject Ho if (test statistics) (critical value)

  Fail to Reject Ho if (test statistics) >(critical value)

Here, (test statistics = -1.23) > (critical value=-1.28)

Hence Fail to reject Ho

There is insufficient evidence, at the given significance level, to reject H₀; or we fail to reject H₀.