Originally Posted by

**samprasbackhand** Hi, I missed both of my stat classes last week due to illness and I have homework that's due for it, and I have absolutely no idea how to do it now, all because I couldn't go to class...can someone teach me how to do these problems?

1. A machine that fills vegetable oil jugs is designed to fill each jug with 80 ounces of oil with a standard deviation of 3.25 ounces. A quality control manager at the company is investigating a possible problem (potential underfill) with the machine. that the machine is not filling the jugs with the prescribed amount of vegetable oil. If the true average amount of fill is 80 ounces, what is the probability, in a random sample of 25 jugs from the production line, of getting a sample mean of between (and including) 78.9 and 81.2 ounces?

2. Suppose the time necessary to complete an examination is known to have a mean of 45 minutes and a standard deviation of 4 minutes. A random sample of 64 students is selected. Find the distribution of the sample mean, X-bar.

3. A population consists of four numbers, 1, 2, 3, and 4. Suppose we randomly select two of those four numbers without replacement and compute the sample mean of the two numbers selected. Find the sampling distribution of the sample mean, X-bar.

4. Refer to Question #3. Describe the shape of the sampling distribution.

5. Suppose you wish to test H0 : μ = 10 vs H1 : μ ≠ 10 and you calculate a test statistic value of z = 2.45. Calculate the p-value.

(Your answer should be in decimal format, using four decimal places and a 0 before the decimal point.)

6. Refer to Question #5. What is the appropriate conclusion?

7. 3.88, 5.56, 6.04, 2.80, 4.90, 4.68, 5.36, 4.16, 2.04, 3.80, 4.40, 5.10

From this data, the mean and standard deviation were found to be 4.3933 and 1.1518, respectively.

Set-up the null and alternative hypotheses

8. Refer the Question #7. Calculate the value of the test statistic. (Your answer should be in decimal format, using two decimal places and a 0 before the decimal point.)

9. Refer to the Question #7. Set-up the appropriate rejection region using α = 0.05.

10. Refer the Questions 7, 8 and 9. What is your conclusion?