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?
|
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?
|
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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