Recently,a large academic medical center determined that 9 of 25 employees in a particular position were female,whereas 59%of the employees for this position in the general workforce were female.At the 0.01 level of significance,is there evidence that the proportion of females in this position at this medical center is different from what would be expected in the general workforce? H0:π=0.59;H1:π≠0.59 , ZSTAT =-2.34 What is the p-value?
Question
Recently,a large academic medical center determined that 9 of 25 employees in a particular position were female,whereas 59%of the employees for this position in the general workforce were female.At the 0.01 level of significance,is there evidence that the proportion of females in this position at this medical center is different from what would be expected in the general workforce? H0:π=0.59;H1:π≠0.59 , ZSTAT =-2.34 What is the p-value?
Solution
The p-value is the probability that you have falsely rejected the null hypothesis.
Z-scores are measures of standard deviation. For ZSTAT = -2.34, the p-value can be found using a Z-table or online calculator.
A Z-score of -2.34 corresponds to a p-value of 0.0194.
However, since this is a two-tailed test (because we're looking for a difference in either direction from the expected proportion), we need to double this p-value.
So, the p-value for this test is 0.0194 * 2 = 0.0388.
At the 0.01 level of significance, we would reject the null hypothesis if our p-value was less than 0.01. Since 0.0388 is greater than 0.01, we do not reject the null hypothesis.
Therefore, there is not enough evidence at the 0.01 level of significance to say that the proportion of females in this position at this medical center is different from what would be expected in the general workforce.
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