The average pre-school cost for tuition fees last year was ₱14,200. The following year, 20
institutions had a mean of ₱13,100 and a standard deviation of ₱2,250. Is there sufficient evidence
at 𝛼= 0.10 level of significance to conclude that the mean cost has increased?
SOLUTION:
Step 1 𝐻0:____________________________________________________
𝐻𝑎: ____________________________________________________
Step 2. 𝛼= _________
Step 3. 𝑧𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 = _________
Step 4. Compute the test statistic.
Step 5. Decision Rule:_______________________
Step 6: Conclusion.
The following null and alternative hypotheses need to be tested:
This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.
Based on the information provided, the significance level is degrees of freedom, and the critical value for a right-tailed test is
The rejection region for this right-tailed test is
The t-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value for right-tailed, degrees of freedom, is and since it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population mean
s greater than 14200, at the significance level.
Comments