My hypothesis test is a lower tail test. and this is the data i developed for my p values and z statistics and I have a feeling its wrong because shouldnt all the z statistics be negative? I am very confused.
remeber each answer is only to two decimals:
Firm 1: pvalue 0.99, z statistic 2.65
firm2 : pvalue 0.04, z statistic -1.73
firm3: pvalue 0.01, z statisct -2.23
firm4: pvalue 0.00 z staitics -3.16
firm5 p value 0.00, z statistic -3.82
Yes, if you are talking about the "lower end," the Z scores should all be negative.
However, firm 2 = -1.75
Other data is in error. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the Z scores. P value of zero cannot have two different Z scores.
Based on the information you provided, it seems like some of the p-values and z-statistics are not consistent with each other. In a lower tail test, the alternative hypothesis is that the true parameter value is less than the hypothesized value. Therefore, the z-statistics should be negative for all firms if their p-values suggest rejection of the null hypothesis at a specified significance level.
Let's go through each firm's data:
1. Firm 1: p-value = 0.99, z-statistic = 2.65
- The p-value of 0.99 suggests that there is insufficient evidence to reject the null hypothesis.
- However, the positive z-statistic of 2.65 does not align with a lower tail test. It should be negative.
2. Firm 2: p-value = 0.04, z-statistic = -1.73
- The p-value of 0.04 suggests that there is evidence to reject the null hypothesis at a 5% significance level.
- The negative z-statistic of -1.73 aligns with a lower tail test.
3. Firm 3: p-value = 0.01, z-statistic = -2.23
- The p-value of 0.01 suggests strong evidence to reject the null hypothesis at a 1% significance level.
- The negative z-statistic of -2.23 aligns with a lower tail test.
4. Firm 4: p-value = 0.00, z-statistic = -3.16
- The p-value of 0.00 suggests strong evidence to reject the null hypothesis at any reasonable significance level.
- The negative z-statistic of -3.16 aligns with a lower tail test.
5. Firm 5: p-value = 0.00, z-statistic = -3.82
- The p-value of 0.00 suggests strong evidence to reject the null hypothesis at any reasonable significance level.
- The negative z-statistic of -3.82 aligns with a lower tail test.
To summarize, there seems to be an error in the data for Firm 1, where the z-statistic is positive instead of negative. This inconsistency can lead to confusion and should be addressed by rerunning the analysis or verifying the correctness of the reported values.