Consider the following hypothesis test: A sample of 50 provided a sample mean of
ID: 3380631 • Letter: C
Question
Consider the following hypothesis test: A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3. Compute the value of the test statistic (to 2 decimals). What is the p-value (to 4 decimals)? Using alpha =.05, can it be concluded that the population mean is not equal to 15? Using alpha =.05, what are the critical values for the test statistic? (to 2 decimals) (+ or -) State the rejection rule: Reject H_0 if z is - Select your answer - the lower critical value and the upper critical value. Can it be concluded that the population mean is not equal to 15?Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u = 15
Ha: u =/ 15
As we can see, this is a two tailed test.
Getting the test statistic, as
X = sample mean = 14.15
uo = hypothesized mean = 15
n = sample size = 50
s = standard deviation = 3
Thus, z = (X - uo) * sqrt(n) / s = -2.003469213 [ANSWER]
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B)
Also, the p value is
p = 0.045126949 [answer]
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C)
As P < 0.05, YES, we can conclude that the populaiton mean is not equal to 15. [ANSWER, YES]
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d)
At 0.05 level, the critical values are
z = +/- 1.96 [ANSWER]
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e)
Reject Ho if z is LESS THAN the lower critical value and GREATER THAN the upper critical value.
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f)
YES, becasue zstat < -1.96. [ANSWER]
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