What is wrong with the statement:
It is believed that the proportion of Middle School teachers who leave the profession within 5 years is different from the proportion of High School teachers who leave the profession within 5 years. Test with a level of significance of 0.05.
Hypotheses: Let Pm = population proportion of Middle School teachers who leave the profession within 5 years and let PH = the population proportion of high school teachers who leave the profession within 5 years.
Ho: Pm = PH Ha: Pm ≠ PH
Data: From a random sample of 200 middle school teachers 75 left the profession within 5 years. From a random sample of 250 high school teachers 71 left the profession within 5 years.
Test statistic: Z = 2.05, P-value = 0.040
Decision: reject the null hypothesis
Statement: The sample of data provided enough information to claim Pm is different from Ph.
If you math is correct, I agree.
The statement itself is not necessarily wrong, but there are a few things that need to be clarified to make it more accurate and valid.
1) The statement should clearly state that the hypothesis test is done with a level of significance of 0.05. This is important because the significance level determines the threshold for accepting or rejecting the null hypothesis.
2) The statement should provide the sample means or proportions that were used to calculate the test statistic and the p-value. In this case, the statement mentions the test statistic (Z = 2.05) and the p-value (0.040), which indicate the strength of evidence against the null hypothesis.
3) The statement should clearly mention the null and alternative hypotheses. In this case, the null hypothesis (Ho) is that the proportion of Middle School teachers who leave the profession within 5 years (Pm) is equal to the proportion of High School teachers who leave the profession within 5 years (PH), and the alternative hypothesis (Ha) is that Pm is not equal to PH.
4) The statement should provide the data and sample sizes that were used to calculate the sample proportions. In this case, the statement provides the number of teachers who left the profession within 5 years from random samples of 200 Middle School teachers (75 left) and 250 High School teachers (71 left).
5) Finally, the conclusion should be based on comparing the p-value to the significance level specified in the statement. If the p-value is less than the significance level (0.05 in this case), then we reject the null hypothesis. So, the statement correctly concludes that the null hypothesis is rejected based on the given p-value of 0.040, which is less than 0.05.
Therefore, a revised and more accurate statement could be:
Based on the hypothesis test conducted at a significance level of 0.05, using a random sample of 200 Middle School teachers (with 75 leaving the profession within 5 years) and a random sample of 250 High School teachers (with 71 leaving the profession within 5 years), the p-value of 0.040 indicates significant evidence against the null hypothesis. Thus, we reject the null hypothesis and conclude that the proportion of Middle School teachers who leave the profession within 5 years is different from the proportion of High School teachers who leave the profession within 5 years.