# Answer to Question #350962 in Statistics and Probability for sergu

Question #350962

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

1
2022-06-16T10:27:32-0400

The following null and alternative hypotheses need to be tested:

"H_0:\\mu=24672"

"H_1:\\mu\\not=24672"

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 "\\alpha = 0.01," "df=n-1=34" and the critical value for a two-tailed test is "t_c =2.728394."

The rejection region for this two-tailed test is "R = \\{t:|t|>2.728394\\}."

The t-statistic is computed as follows:

"t=\\dfrac{\\bar{x}-\\mu}{s\/\\sqrt{n}}=\\dfrac{26343-24672}{3251\/\\sqrt{35}}=3.0408"

Since it is observed that "|t|=3.0408>2.728394=t_c," it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value for two-tailed, "df=34" degrees of freedom, "t=3.0408" is "p= 0.004521," and since "p=0.004521<0.01=\\alpha," it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean "\\mu" is different than 24672, at the "\\alpha = 0.01" significance level.

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