Show your complete solutions and box your final answers.

1. The graph of the t-distribution with 15 degrees of freedom is shown below.

Find the value of t such that the:

a. shaded area on the left is equal to 0. 05

b. shaded area on the right is 0.1

c. Total shaded area is 0.02

d. Area to the left of t^1 = 0.95

2. Find the 5th percentile of a t-distribution with 28 degrees of freedom.

3. The area to the left of t^1 is 0.995, what is the value of t^1?

Analyze the given situations and do what is asked in each item. Include your complete solutions and box your

final answers.

1. The mean score of a random sample of 35 Grade 11 students who took the first periodic test is calculated to be 86. The population variance is known to be 0.10. a) Find the 95% confidence interval for the mean of the entire Grade 11 students.

b) Find the lower and upper confidence limits.

2. The mean and standard deviation of the scores of a random sample of 45 Grade 10 students who took the final test are calculated to be 76 and 12.5, respectively. Find the 95% confidence interval for the mean of the entire Grade 10 students.

3. Suppose a student measuring the boiling temperature of a certain liquid observes the readings (in degrees Celsius) 102.5, 101.7, 103.1, 100.9, 100.5, and 102.2 on 6 different samples of the liquid. He calculates the sample mean to be 101.82. If he knows that the standard deviation for this procedure is

1.2 degrees, what is the length of confidence interval for the population mean at a 90% confidence level?

4. Researchers are interested in the average heart rate of male college students. Assume a random sample of 130 male college students were taken from 200 students for the study. Find a 95% confidence interval for the actual proportion of students.