4. Data were collected on student teachers relative to their use of certain teaching strategies that had been presented to them in preservice education. There were 28 student teachers who had learned to use the strategies (9 in 1979, 9 in 1980, and 10 in 1981). In 1978 there were 6 teachers who did not learn to use the strategies, and they were used as a control group. The investigator recorded the average number of strategies used per week by each of the student teachers during their student teaching assignments. The investigator wanted to know whether the number of strategies used by the student teachers was different among the years.

e. Compute the 95 % confidence interval estimates of the treatment means.

f. Test the hypothesis of no differences among means of the four treatments with the F test at the .05 level of significance.

g. Write the normal equations for the data.

In a distribution, X=75, and standard deviation=5. if z=3 is the maximum z score value of a data value in the distribution, and z=-2 is the minimum z score value of data in the distirbution, then the range of the distiribution is equal to?

show work and explain

The height of women ages 18 to 24 are approxiametly bell shaped with X=64.5 inches and S=2.5 inches. according to the empirical rule, approximately what percentage of the women's height would you expect to fall between:

*explain and show work

a) 62 and 67 inches?

b) 59.5 to 69.5 inches?

c) 57 to 72 inches?

d) if there was a height equal to 77 inches, could you consider such a height and outlier?explain

Show all of your work. No credit will be given if there is no work. Simplify if possible, unless noted.

Setup:

• Suppose the probability of a part being manufactured by Machine A is 0.4

• Suppose the probability that a part was manufactured by Machine A and the part is defective is 0.12

• Suppose the probability that a part was NOT manufactured by Machine A and the part IS defective is 0.14

Questions To Answer: 1. (2 pts) Find the probability that a part is defective given that it was made by Machine A.

2. (2 pts) Find the probability that a part is defective.

3. (4 pts) Are the states of a part being made by Machine A and being defective independent? Circle your answer and state your reason. YES, they are independent NO, they are NOT independent Reason:

4. (2 pts) Find the probability that Machine A produced a specific part, given that the part was defective. Round your final answer to 2 decimals, if needed.

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals. A random sample of 50 home theater systems has a mean price of ​$149.00. Assume the population standard deviation is ​$18.70.

Construct a​ 90% confidence interval for the population mean. The​ 90% confidence interval is ​( _____​, ______​). ​(Round to two decimal places as​ needed.)

Normal (or Gaussian) distributions are widely used in practice because many sets of observations follow a bell-shaped curve. In statistics, the normal distribution is one of the main assumptions in statistical inferences, such as confidence intervals and hypothesis tests.

After conducting some basic searches using scholarly articles, explain how normal distributions are used in business analytics. Your findings must include:

1. The problem background
2. Why a normal distribution is used
3. How is a normal distribution used?
4. What are the results?

Dr. Harmon expected that her neurotic patients would come significantly earlier to all scheduled appointments compared to other patients, and planned to run a one-tailed test to see if their arrival times were much earlier. Unfortunately, she found the opposite result: the neurotic patients came to appointments later than other patients. What can Dr. Harmon conclude from her one-tailed test?

a) There is no evidence that neurotic patients come to appointments significantly earlier than other patients.

b) Neurotic patients come to appointments significantly earlier than other patients.

c) Neurotic patients come to appointments significantly later than other patients.

d) Non-neurotic patients come to appointments significantly earlier than neurotic patients.

In Excel, the RAND function generates random numbers between 0 and 1

compute the expectation and Standard deviation.

Hints

a = 0 , b = 1

P(x1<= X <= x2) = F(x2) - F(x1)

Suppose you toss a fair coin 10 times.

(a) Calculate the probability of getting at least 6 heads, using the exact distribution.

(b) Now repeat the calculate above, but approximate the probability using a normal random variable. Do your calculation both with and without the histogram correction. Which one is closer to the true answer?

Now suppose you toss a fair coin 1000 times.

(c) What is the probability of getting at least 520 heads? You can approximate this using a normal with the appropriate mean and variance. Do this with and without the histogram correction. (Does it matter if you use this correction?)

(d) What is the probability of getting at least 600 heads? Calculate this however you want.

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 20.

Use the empirical rule to determine the following:

​(a) What percentage of people has an IQ score between
60 and 140?

​(b) What percentage of people has an IQ score less than
60 or greater than 140?

​(c) What percentage of people has an IQ score greater than 160?

An engineer has carefully measured the spacing between anchor bolts (in mm) as:
19   23   21   21
19   13   26   15
30   30   17   24
20   16   24   20
Find:
a. The 90 percent CI for µ
b. The 80 percent CI for µ
c. The 99 percent CI for µ assuming σ = 4.1 mm is known

OptiJet Airlines provide daily service for commuters traveling from South to MidWest. One of the fare classes for this flight has been set at $250. The airline has set aside a capacity of 25 passengers in this fare class. Historical passenger demand for these seats in this fare class has been fit to a normal distribution with mean 27.18 and standard deviation 3.14. If demanded, the airline will typically accept more reservations than the seat capacity since only 90% of all customers who have a reservation show up for the flight. This policy is called overbooking. If the flight is overbooked, anyone who shows up but does not receive a seat on the plane receives $350 in compensation in addition to a full refund of the ticket price. The variable cost of transporting a passenger and his/her luggage on this flight is $100. The fixed cost of operating the flight is $2,500. To maximize expected profit from operating this flight, how many reservations for the flight should this airline accept? Develop a simulation model in the spreadsheet file. What would be the best strategy for the airline?

Describe the difference between standard deviation and standard error.