1. The average score in the entrance examination in Mathematics at Sto.
Rosario National High School is 80 with a standard deviation of 10.A
random of 40 students was taken from this year's examinees and
was found to have a mean score of 84.
Is there a significant difference between the known mean and the
sample mean? Test at a= 0.05
Solution :
Step 1. H0: = 80 : There is no significant difference
hypothesized and the sample mean.
H1: 80 :
Step 2. Level of significance. a = 0.05.
Step 3. two tailed test, find the critical value. Zt =
4. Compute the test-statistic value:
5. Step :
6. Conclusion:
The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.
Based on the information provided, the significance level is and the critical value for a two-tailed test is
The rejection region for this two-tailed test is
The z-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is rejected.
Using the P-value approach:
The p-value is and since it is concluded that the null hypothesis is rejected.
Therefore, there is enough evidence to claim that the population mean
is different than 80, at the significance level.
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