Imagine you created a new drug that you think will increase IQ. As a responsible researcher, you want to test this drug to see if it does, indeed, significantly alter IQ scores. To that end, you recruit a sample of n=9 individuals and give them the new drug. After one month, you record their IQ scores and find that the mean IQ of the sample is 109. We know that the population distribution of IQ scores has a mean of μ=100 with a standard deviation of σ=15. Use this data to run a full hypothesis test using the z-score hypothesis test to test the hypothesis that people who take your drug have significantly different IQ scores compared to the whole population (alpha of α=0.05, two-tailed test). For your answer to this question, write a paragraph IN YOUR OWN WORDS that contains all of the following information:

Hypotheses

Critical values

Final z-score answer

Conclusion about the null hypothesis

Written summary of the conclusions that can be made from this study

1. When identical parts are being manufactured. They vary from one another. If the variation is normally distributed if:

a) is natural and is to be expected

b) indicates the parts do not meet quality standards

c) indicates an unstable process is developing

2. Probability tells us:

a) how often something actually occurs

b) how often something is expected to occur

c) the number of random samples it takes for an event to occur

3. Unnatural variation is normally the result of:

a) expected variation in the process

b) assignable causes

c) product design choices

4. A histogram is a graph of:

a) the past history of the process

b) machine capability

c) how often events or measurements occur

5. The normal distribution curve:

a) is a picture of how products are distributed from a stable set of conditions

b) provides accurate information about specification limits

c) allows us to identify causes of variation

6. The mean of a sample taken from a population:

a) is written as x

b) is the result of measuring all the individuals

c) determines process capability

7. Range is:

a) the number of times an event occurs

b) the difference between highest and lowest values

c) shown on an x chart

8. The variability of a group is described by:

a) standard deviation

b) population totals

c) the value between the first and last piece produced

9. A “quality” product is one that:

a) is within the specification limits

b) meets the needs and expectations of the customer

c. uses geometric dimensioning and tolerancing

10. Statistical Process Control:

a) tracks the variability of products or services

b) will solve he majority of quality related problems

c) is most useful during 100% inspection

11. The normal distribution of average is:

a) larger than the distribution of individuals

b) narrower than the distribution of individuals

c) the same as the distribution of individuals

12) A product’s key quality characteristics are monitored:

a) during final inspection

b) within +- 0.001

c) using control chart

13. Control limits on an x are:

a) the statistical words for blueprint tolerances

b) based upon the distribution of sample averages

c) used to determine process capability

14) Process capability studies:

a. given information about how a process is behaving

b) are most effective in determining whether or not SPC works

c) require that a single machine be capable of producing at least 2 different parts

15) Values plotted as points on an x chart are:

a) individual values

b) specification limits

c) sample values

16. The pattern of points on an x chart should show a normal distribution that:

a) closely parallels individual measurement

b) shows percent defective

c) is within +- 3 sigma

Angelica Reardon received a 5-year non-subsidized student loan of $15,000 at an annual interest rate of 6.7%. What are Angelica's monthly loan payments for this loan after she graduates in 4 years? (Round your answer to the nearest cent.)

A simple random sample of 10 items resulted in a sample mean of 30. The population standard deviation is σ=20.

a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.
( ,  )

b. Assume that the same sample mean was obtained from a sample of 100 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places.
( ,  )

Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 75% chance of answering any question correctly. (Round your answers to two decimal places.)

(a)

A student must answer 45 or more questions correctly to obtain a grade of A. What percentage of the students who have done their homework and attended lectures will obtain a grade of A on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question.

%

(b)

A student who answers 34 to 39 questions correctly will receive a grade of C. What percentage of students who have done their homework and attended lectures will obtain a grade of C on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question.

%

(c)

A student must answer 28 or more questions correctly to pass the examination. What percentage of the students who have done their homework and attended lectures will pass the examination? Use the normal approximation of the binomial distribution to answer this question.

%

(d)

Assume that a student has not attended class and has not done the homework for the course. Furthermore, assume that the student will simply guess at the answer to each question. What is the probability that this student will answer 28 or more questions correctly and pass the examination? Use the normal approximation of the binomial distribution to answer this question.

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 2643 miles, with a standard deviation of 368 miles. If he is correct, what is the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles? Round your answer to four decimal places.

1. There are multiple sections of 3 classes that have to be offered. Class A has an average enrollment of 120 per term. Class B has an average of 100 students per term and Class C has an average enrollment of 85 students per term. The rules for opening and cancelling sections are as follows:

1. Any section of this class must have at least 15 students to run. Any less than this and the section is cancelled.
2. Each section has a maximum enrollment of 45 students.
3. A new section will open up when the previous section (s) have an average enrollment of 40.
4. A new section will open up to accommodate department regulations on staffing.

For each class run a simulation using your chosen distribution and determine the following:

1. Given that anytime enrollment in a class reaches over 175 students, there will be 5 sections of class, what is the probability of this happening with each class?

Class A =

Class B =

Class C =

ii)    Given that anytime enrollment in a class reaches 135 students to 180 students, there will be 4 sections of class, what is the probability of this happening with each class?

Class A =

Class B =

Class C =

3. Given that anytime enrollment in a class reaches 95 students to 120 students, there will be 3 sections of class, what is the probability of this happening with each class?

Class A =

Class B =

Class C =

4. If a third section of Class C opens when enrollment goes above 80, and it gets cancelled when enrollment is below 95, How often does the third section get cancelled? (Enrollment is between 80 and 95)

5. Based upon the probabilities you found above, how many sections of each class do you offer? 2, 3, 4 or 5?

Class A =

Class B =

Class C =

Using the number of sections, you found above create a schedule that maximizes the quality of teaching these classes. Full Time profs must teach 3-4 sections. Part time profs must teach 1-2 sections.

6. What is the minimum number of sections (total) that need to be offered?

7. What is the maximum number of sections (total) you can offer?

Professor Data is below:

Given your answers in part v, and possibly modified by your answers in part vi, what is the quality score of your department’s teaching?

How many sections of each class do the professors teach?

Which of the following statements is correct regarding the null and alternative hypothesis?

a) the alternative hypothesis is the one that we want to reject

b) the null hypothesis should be identified as the one without an equality relationship

c) one should dichotomize(divide in two) the possible values of the parameter on the basis of the decision that must be made, then identify the null and alternative hypotheses accordingly

d) all of the above

Historically, 20% of graduates of the engineering school at a major university have been women. In a recent, randomly selected graduating class of 210 students, 58 were females. Does the sample data present convincing evidence that the proportion of female graduates from the engineering school has shifted (changed)? Use α = 0.05.

***I ALREADY HAVE A-E ANSWERED***
A.State the null and alternative hypotheses to be tested and indicate whether the test is left-tailed, right-tailed or two-tailed.

B. List the conditions that should be met in order to proceed with the hypothesis test and explain why (or show how) they are met.

C.Compute the test statistic and p-value for the hypothesis test and sketch the distribution of the test statistic, if the null hypothesis is true. Identify - label and shade - the region(s) represented by the p-value. Show your calculation(s).

D.Make a statistical decision about the null hypothesis (i.e. fail to reject H0 or reject H0), using the p-value approach. Justify your answer.

E.Write your conclusion in the context of the problem.

***I NEED F AND G ANSWERED***

F.Suppose we were to instead use a confidence interval to test if the proportion of female graduates from the engineering school differs from 20%.

-What would be the confidence level?

-Construct the confidence interval and explain how it supports your decision/conclusion made in (d) and (e). Show your calculation(s).

G.Determine the critical value(s) for this hypothesis test and explain how you would use it to come to the same decision/conclusion.

Suppose N = 12 and r = 4. Compute the hypergeometric probabilities for the following values of n and x. If the calculations are not possible, please select "not possible" from below drop-downs, and enter 0 in fields.

a. n = 3, x = 2 (to 4 decimals).

b. n = 2, x = 2 (to 4 decimals).

c. n = 3, x = 0 (to 4 decimals).

d. n = 6, x = 3 (to 4 decimals).

e. n = 5, x = 5 (to 4 decimals).

Dear Students:

I have recently been employed by HMS Nautical Inc to work on their submarine program. I have only some basic data to work with and no idea how to use it to get the information I need.

Here is what I know. First, I know that our Subs have a maximum running depth of 500 feet below sea level. I also know that a sub functioning at acceptable levels should be able to reach maximum depth in 10 minutes. Finally I know that I need to multiply the decent by a factor of 5 to achieve an accurate model. I also have a chart that lists times and depths for the sub.

Finally, I know that the sub follows a quadratic model when it descends and then ascends.

I have been told that you will be able to take this data and make sense of it. I would like a model for the path of the submarine as it descends to its running depth and then returns to the surface. I want to be able to use this model to predict where the sub will be at any time during its decent/ascent cycle. I would also like to know after how many minutes I should expect the sub to breech the surface of the water again.

Please explain clearly how you came up with the model so that I can repeat the process for new additions to our fleet of submarines. I appreciate any help you can give me in this matter. I would like your response returned to me either as a business letter or a narrated PowerPoint presentation.

Sincerely,

Nemo Hook

HMS Nautical Inc.

A simple random sample with n=56 provided a sample mean of 22.5 and a sample standard deviation of 4.3.

a. Develop a 90% confidence interval for the population mean (to 1 decimal).

( , )

b. Develop a 95% confidence interval for the population mean (to 1 decimal).

( , )

c. Develop a 99% confidence interval for the population mean (to 1 decimal).

( , )

A. type of research design (between-subjects or within-subjects)

b. Define the dependent variable.

c. Define the independent variable and its levels

d. Fill in the missing cells of the ANOVA F-table

e. Determine the critical value at a .05 level of significant for the F-value and decide whether the ANOVA result is statistically significant (see Table C.3 in Appendix C of the textbook)

f. Calculate and interpret the eta-squared measure of effect size (if it is a between-subjects designs) or the partial eta-squared measure of effect size (if it is a within-subjects design).

Case 1: A teacher was curious about if his students’ test scores would be affected by how they learn about important science experiments. To look into the situation, he randomly assigned students to 1of 3 groups: students in the first group read about an experiment, students in the second group watched a video, and students in the third group actually conducted the experiment. At the end, all students were given a test about the experiment.

A psychologist is planning a study to test whether people are more likely to call events "natural" that are otherwise frequently attributed to "supernatural forces" if they have seen a particular film critical of "superstitions." Discuss the three things the psychologist should consider in order to maximize power for the planned study. Be specific, i.e., describe the statistical principles and explain how each works to increase power