# P-Value â€“ Actual significance level

• P-value
• The probability of obtaining an observed value of x (from the sample) is as high as $20,000 or more when actual populations mean (Î¼) is only$19,000 = 0.00621
• This value is sometimes called the actual significance level, or the p-value
• Calculated probability of rejecting the null hypothesis (H0) when that hypothesis (H0) is true (Type I error)
• The actual significance level of 0.00621
• in this case means that the odds are less than 62 out of 10,000 that the sample mean income of $20,000 would have occurred entirely due to chance (when the population mean income is$19,000)

Example

Which of the following statements regarding hypothesis testing is/are true?
If the significance level is more than the p-value, the null hypothesis is rejected
A decrease in the level of type I error causes a decrease in Type II error as well
Type I error is the error when a false null hypothesis is not rejected
Systematic error is caused by non-random variations due to unknown sources

1. I only
2. I and IV
3. I and III
4. I, II and IV

Solution

A.
II is false. A decrease in the level of Type-I error increases the Type-II error
III is false. Type I error is when a true null hypothesis is rejected

Example

Consider an exam taken by 15,000 FRM candidates. Mean score for the exam was 64 for all the 6,400 candidates who studied at least 250 hours in the preparation of the exam. Assuming a population standard deviation of 16. What would be 99% confidence interval for the mean score on the exam for the 6400 candidates who study at least 250 hours? (Given Z0.005 =2.575)

1. 64 Â± 0.52
2. 64 Â± 0.80
3. 64 Â± 5.15
4. 64 Â± 8.05

Solution

A.
The confidence interval: Î¼ Â± Z * (Ïƒ/sqrt(n))
= 64 Â± 2.575 * 16/sqrt(6400)
= 64 Â± 0.515