Question

# A sample of size 234, taken from a normally distributed population whose standard deviation is known...

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

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.

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