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, H_{0} is that μ ≥ 76 and we want
to test the alternative hypothesis, H_{1}, that μ
< 76, with level of significance α = 0.1.
a)  What type of test would
be appropriate in this situation?

b) What is the critical value? (for a twotailed
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 H_{0}?

n= 234, =5.70, =75.54, =76, =0.10
H0: μ ≥ 76
H1: μ < 76
a) A lefttailed 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 H_{0}; or we fail to reject H_{0}.
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