A medical centre reports that the average cost of rehabilitation for stroke victims is 24672 BD. To see if the average cost of rehabilitation is different at a particular hospital, a researcher selects 35 victims at random and find the average cost is 26343 BD. Standard deviation is 3251 BD. At α=0.01, can it be concluded that the average cost of rehabilitation at a particular hospital is different form 24672 BD
The following null and alternative hypotheses need to be tested:
This corresponds to a two-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 and the critical value for a two-tailed test is
The rejection region for this two-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 two-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 different than 24672, at the significance level.
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