Exercises
Adapted from Freedman, Pisani and Purves (1997) “Statistics”, 3rd edition, W. W. Norton & Company, New York.
1. True or False and explain:
a. A “highly significant” result cannot possibly be due to chance.
b. If a difference is “highly significant”, there is less than a 1% chance for the null hypothesis to be right
c. If a difference is “highly significant”, there is better than a 99% chance for the alternative hypothesis to be right.
Guidelines:
If a p-value is < 5%, the result is called “statistically significant”.
If a p-value is < 1%, the result is called “highly significant”.
2. For a t-statistic (t) of 2.35 with 99 degrees of freedom, the p-value is ~.01. True or False and explain:
a. If the null hypothesis is right, there is only 1% of getting a t bigger than 2.35.
b. The probability of the null hypothesis given the data is 1%.
3. True or False and explain:
a. The observed significance level depends on the data.
b. If the observed significance level is 5%, there are 95 chances in 100 for the alternative hypothesis to be right.
4. Many companies are experimenting with “flex-time”, allowing employees to choose their schedules within broad limits set by management. Among other things, flex-time is supposed to reduce absenteeism. One firm knows that in the past few years, employees have averaged 6.3 days off from work (apart from vacations). This year, the firm introduces flex-time. Flex-time chooses a simple random sample of 100 employees to follow in detail and at the end of the year, these employees average 5.5 days off from work and the SD is 2.9 days. Does this mean that flex-time reduced absenteeism? Or is this chance variation? (Use table for calculations and explain in terms of your null hypothesis)
5. Repeat exercise #4 for a sample average of 5.9 days and an SD of 2.9 days.