A statistic student used a computer program to test the null hypothesis Ho:p=.5

Question

A statistic student used a computer program to test the null hypothesis Ho:p=.5 against the one-tailed alternative, Ha:p>>5. A sample of 500 observation are input into SPSS, which returns the following results: z=.44, two tailed p-value=.33.

a. The student concludes, based on the p-value, that there is a 33% chance that the alternative hypothesis is true. Do you agree? if not, correct the interpretation.

b.How would the p-value change if the alternative hypothesis was two-tailed, Ha:p  .5? interpret this p-value.

Explanation / Answer

a) p-value = 0.33 < z-value = 0.44 then we reject null hypothesis and say that alternative hypothesis is true . So as we got p-value 0.33 then we say there is 33% chance that alternative hypothesis is true. Thus interpretation is correct.

b) If we want to do two-tailed hypothesis testing then alternative hypothesis will change as Ha:p 0.5 and p-value would be same as p-value =0.33 and then p-value 0.33 < z-value =0.44 , so we will reject the null hypothesis as interpret as alternative hypothesis is true but the chance of alternative hypothesis to be true can be less than 33% or more than 33%.

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