Use the information below to answer Questions 1 through 4.
Given a sample size of 34, with sample mean 660.3 and sample standard deviation 104.9, we perform the following hypothesis test.
Null Hypothesis [pic]
Alternative Hypothesis [pic]
1. What is the test statistic?
2. At a 5% significance level (95% confidence level), what is the critical value in this test? Do we reject the null hypothesis?
3. What are the border values in terms of the sample mean between acceptance of Ha and rejection of this hypothesis (Ho)? (note you will have a value less than the mean and a value greater than the mean since a tool tailed test. Draw it out ...view middle of the document...
Determine SSxx, SSxy, and SSyy.
11. Find the equation of the regression line. What is the predicted value when [pic]
12. Is the correlation significant at 5% significance level (95% confidence level)? Why or why not?
Use the data below to answer Questions 13 through 15.
A group of students from three universities were asked to pick between three lest favorite subjects as their major, as if they really had to. The results, in number of students, are listed as follows:
| |Mathematics |Physics |Engineering |
|St. John |40 |50 |20 |
|La Salle |47 |45 |18 |
|Loyola |30 |25 |55 |
Supposed that a student is randomly selected from the group mentioned above.
13. What is the probability that the student is from Loyola or chooses Mathematics?
14. What is the probability that the student is from La Salle, given that the student chooses Physics?
15. What is the probability that the student is from St. John and chooses Engineering?
Use the information below to answer Questions 16 and 18.
High precision titanium spheres are popular components in manufacturing of ball bearings. A factory has ordered a shipment of 5000 titanium spheres from aboard. It is found that the shipment has a mean radius of 1.5 cm with a standard deviation of .03 cm in the shipment.
16. How many titanium spheres have radii between 1.48 cm and 1.52 cm?
17. What is the probability that a randomly selected titanium sphere has radius greater than 1.58 cm?
18. A quality inspector randomly selected 64 titanium spheres from the shipment.
a. What is the probability that the 64 randomly selected titanium spheres have a mean radius less than 1.49 cm?
b. Do you come up with the same result in Question 17? Why or why not?
19. Suppose that in a cartoon of 12 eggs, there are 4 cracked ones. In a draw without replacement, if 3 eggs are picked, what is the probability that all 3 are cracked?
Use the information below to answer Questions 21 and 21.
Benford's law, also called the first-digit law, states that in...