The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages. 1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8

2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4

3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9

1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0

1.2 1.8 2.4

(a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = % s = %

(b) Compute a 90% confidence interval for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.) lower limit % upper limit %

(c) Compute a 99% confidence interval for the population mean μ of home run percentages for all professional baseball players. (Round your answers to two decimal places.) lower limit % upper limit %

1. The desired percentage of Silicon Dioxide in a certain type of aluminous cement is 5.5. Sixteen independently obtained samples are analyzed, the sample statistics are: sample mean, x=5.25 and, sample standard deviation, s=0.3. We need to test if the true mean Silicon Dioxide percentage significantly differs from 5.5.

1. Write down the null and alternative hypotheses to be tested. Clearly define the terms used.

2. What is the type of statistical test procedure that should be used to test the hypotheses? Explain.

3. Construct a 95% confidence interval. Test the hypotheses using the confidence interval. Interpret the test result clearly.

4. Test the hypotheses using the Test Statistic / Critical Value method (you must clearly indicate the test statistic, and the critical value(s) use Take α=5%).

5. What is the P value of the test? Test the hypotheses using the P value. Take α=5%.

2. The Izod Impact Test was performed on 20 specimens of PVC pipe. The sample mean is 1.25 and the sample standard deviation is 0.25. We need to test if the true mean Izod impact strength is lesser than 1.5.

1. Write down the null and alternative hypotheses to be tested. Clearly define the terms used.

2. What is the type of statistical test procedure that should be used to test the hypotheses? Explain.

3. Construct a 95% confidence interval. Test the hypotheses using the confidence interval. Interpret the test result clearly

4. Test the hypotheses using the Test Statistic / Critical Value method (you must clearly indicate the test statistic, and the critical value(s) use Take α=5%).

5. What is the P value of the test? Test the hypotheses using the P value. Take α=5%.

Match the Terms:

1. A university planner is interested in determining the percentage of spring semester students who will attend summer school. She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school.
   
   1. Construct a 90% confidence interval estimate for the percentage of spring semester students who will return to summer school.
   2. Construct a 95% confidence interval estimate for the percentage of spring semester students who will return to summer school.

A plant distills liquid air to produce oxygen, nitrogen, and argon. The percentage of impurity in the oxygen is thought to be linearly related to the amount of impurities in the air as measured by the “pollution count” in parts per million (ppm). A sample of plant operating data is shown below:

Perform the FULL linear regression analysis.

Please show how to do in Minitab or excel

Thank you

What is the difference between the effective annual rate and the annual percentage rate, and when should you use which?

Describe the percentage of sales model and its potential pitfalls in the financial planning process .

On a recent trip to the SC DMV, I asked an employee to estimate what percentage of SC drivers arrive to renew their driver’s license with one that is currently expired. She responded that about 30 percent of all such renewals were of this type.

(a) Suppose you observe Y , the number of SC DMV customers seeking renewal to find the first one with an expired license. What is the distribution of Y? Plot the pmf and cdf of Y side by side (like in the notes). (Hint: You can just generate the Y from 1 to 20)

(b) Let W denote the number of SC DMV customers seeking renewal to find the 3rd one with an expired license. What is the distribution of W? Plot the pmf and cdf of W side by side (like in the notes).

(c) Obviously, in parts (a) and (b), you are assuming that Bernoulli trial assumptions hold. State what these are in this application (e.g., think of each customer seeking renewal as a “trial.”)

(d) In parts (a) and (b), find the probability that • among the first 6 customers seeking renewal, none have expired licenses. (Hint: use pgeom(y-1, p)) • you have to observe 10 or more customers seeking renewal to find the 3rd one with an expired license. (Hint: use pnbinom(w-r, r, p))

please include the R code

thanks