A sample of 342 teachers at a particular school has a mean longevity (in months)
ID: 3133862 • Letter: A
Question
A sample of 342 teachers at a particular school has a mean longevity (in months) of 30 with a standard deviation of 4.3 months. The mean longevity of the population of teachers is 41 months. Use this information for the following questions: Test the null hypothesis that the sample mean is significantly different from the population mean at the 95% level of significance. 99% level of significance. What conclusion can be made? If you fail to reject your null hypothesis what conclusion can be made?
Explanation / Answer
Test the null hypothesis that the sample mean is significantly different from the population mean at the 95% level of significance. 99% level of significance. What conclusion can be made?
Formulating the null and alternative hypotheses,
Ho: u = 41
Ha: u =/ 41
As we can see, this is a two tailed test.
Getting the test statistic, as
X = sample mean = 30
uo = hypothesized mean = 41
n = sample size = 342
s = standard deviation = 4.3
Thus, z = (X - uo) * sqrt(n) / s = -47.30829351
Also, the p value is
p = 0
For 95% confidnence:
As P < 0.05, we REJECT THE NULL HYPOTHESIS.
For 99% confidence:
As P < 0.01, we REJECT THE NULL HYPOTHESIS.
Hence, for both confidence levels, there is significant evidence that the mean longevity of teachers in the school examined is different from the mean longevity of the population of teachers. [CONCLUSION]
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If you fail to reject your null hypothesis what conclusion can be made?
There is no significant evidence that the mean longevity of teachers in the school examined is different from the mean longevity of the population of teachers. [CONCLUSION]