In the past, it is generally agreed that a certain standard treatment yields a m

Question

In the past, it is generally agreed that a certain standard treatment yields a mean survival period of 3.5 years cancer patients. Recently, a new treatment is administered to 49 patients and thier duration of survival is recorded. The sample mean and standard deviation of the duration is 3.8 years and 0.7 years, respectively.

1. Set up the null and alternative hypotheses to test whether the new treatment increases the mean survival period.

2. Find the value of the standardized test statistics for the above test

["-3", "3", "0.3", ".06", "1.94"]      

3. Find the P-value for the test and state your conclusion at the significance level of 0.05

["P-value: .9987; Decision: Fail to reject Ho", "P-value: .0013; Decision: Fail to reject Ho", "P-value: .9987; Decision: Reject Ho", "P-value: .0013; Decision: Reject Ho", "P-value: .0026; Decision: Reject Ho"]      

Explanation / Answer

1) for hypothesis: Ho: =3.5

alternate hypothesis: >3.5

2) here std error =std deviation/(n)1/2 =0.7/(49)1/2 =0.1

therefore test statistic z =(X-mean)/std error =(3.8-3.5)/0.1 =3

3) p value for right tail test =0.0013

"P-value: .0013, Decision: Reject Ho"

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