A sociologist believes that it costs more than Php90,000 to raise a child from birth to age one. A random sample of 49 families, each with a child is selected to see if this figure is correct. The average expenses for these families reveal a mean of Php92,000 with a standard deviation of Php4,500.
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 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 rejected.
Therefore, there is enough evidence to claim that the population mean is greater than 90000, at the significance level.
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