The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students' scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation of 8.8. In addition to other qualifications, a score of at least 160 is required for admission to a particular graduate school.

a. What proportion of combined scores can be expected to be over 160?

b. What proportion of combined GRE scores can be expected to be between 155 and 160?

c. What is the probability that a randomly selected student will score less than 150 points?

d. Historically, Department of History at NYU has admitted students whose quantitative GRE score is at least at the 61st percentile. What is the lowest GRE score of the students they admit?

e. Determine the range of scores that make up the middle 95% of the scores.

Twemty subgroups of size 5 are obtained for the purpose of determining trial control limits for mean and an R-chart.

A.) Determine the rial control limits for each chart. B.) Explain why there are so many subgroups averages outside the control limits for the mean chart in spite of the fact that the averages do not vary greatly. C.) What should be done with those subgroups whose averages is beyond the limits. D.) Since the number of points outside the control limits on the mean chart is quite high relative to the number of points that are plotted, what might this suggest about the type of distruibution from which the data could have come.

Hypothesis Testing and Confidence Intervals for Proportions and Hypothesis Test for Difference between Two Means

A pharmaceutical company is testing a new cold medicine to determine if the drug has side affects. To test the drug, 8 patients are given the drug and 9 patients are given a placebo (sugar pill). The change in blood pressure after taking the pill was as follows:

Given drug: 3 4 5 1 -2 3 5 6

Given placebo: 1 -1 2 7 2 3 0 3 4

Test to determine if the drug raises patients’ blood pressure more than the placebo using  = 0.01

Begin this discussion by first stating your intended future career. Then give an example from your intended future career of a Population Mean that you would like to do a Hypothesis Test for. The target Population of your Hypothesis Test activities must be included in your discussion along with the unit of measurement that you are using. As shown in the text your Null and Alternative hypothesis MUST include the symbol for a Population Mean along with your hypothesized claimed numerical value for this parameter.

How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 92% confidence the mean winning's for all the show's players.

34135 29640 26440 19111 34635 24903 20591 34012 33338 23721 19518 32867 21627 17659 28450 34135 19111 20591 23721 21627 29640 34635 34012 19518 17659 26440 24903 33338 32867 28450

Upper confidence limit =

Lower confidence limit =

A television cable company receives numerous phone calls throughout the day from customers reporting service troubles and from would-be subscribers to the cable network. Most of these callers are put “on hold” until a company operator is free to help them. The company has determined that the length of time a caller is on hold is normally distributed with a mean of 3.1 minutes and a standard deviation 0.9 minutes. Company experts have decided that if as many as 5% of the callers are put on hold for 4.8 minutes or longer, more operators should be hired. a. What proportion of the company’s callers are put on hold for more than 4.8 minutes? Should the company hire more operators? Show these probabilities on a sketch of the normal curve. b. At another cable company (length of time a caller is on hold follows the same distribution as before), 2.5% of the callers are put on hold for longer than x minutes. Find the value of x, and show this on a sketch of the normal curve.

. The joint probability density function of X and Y is given by

?(?, ?) = { ??^2? ?? 0 ≤ ? ≤ 2, 0 ≤ ?, ??? ? + ? ≤ 1

0 ??ℎ??????

(a) Determine the value of c.

(b) Find the marginal probability density function of X and Y.

(c) Compute ???(?, ?).

(d) Compute ???(?^2 + ?).

(e) Determine if X and Y are independent

You may need to use the appropriate appendix table or technology to answer this question.

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 probability of 0.70 of answering any question correctly.

(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.

A professor surveyed a simple random sample of undergraduates at his large university. As part of this survey he asked about part time jobs the students had and the amount the students were paid per hour. The resulting data is given in the file “pay_survey.txt” This data is linked from the Moodle.

This data file contains the following variables.

Gender: Male or Female

Year: Year in school as Freshman, Sophomore, Junior or Senior

Pay: hourly rate of pay in dollars

We would like to determine if there is a significant difference between males and females in the hourly pay.

The post:

For this post you should

1. Use SAS to conduct a 2 sample t-test to determine if there is a significant difference between the genders in hourly pay.

Present the output from your SAS program. (You do not need to include the program or data for this post.)

Give an interpretation of the results in practical terms. Clearly explain the p-value and its meaning.

Present the assumptions of the tests you used with an explanation of their meaning in this situation. Also, present your conclusions about the assumptions.

Male Senior 16.82
Female Freshman 3.5
Female Sophomor 12
Female Junior 8
Female Sophomor 9.75
Female Junior 9.25
Female Sophomor 8
Female Junior 9.25
Male Junior 10
Female Junior 8.5
Female Junior 7.5
Female Sophomor 7.25
Female Senior 10
Female Sophomor 7.5
Male Sophomor 10
Female Freshman 8
Female Junior 8.75
Male Sophomor 12
Male Sophomor 7.25
Female Sophomor 15
Male Sophomor 8.25
Male Sophomor 8.5
Female Sophomor 8
Female Sophomor 8.5
Female Sophomor 9
Male Junior 10
Female Sophomor 7.25
Male Sophomor 9
Female Sophomor 7.5
Female Sophomor 8
Female Junior 8
Female Sophomor 8.5
Female Junior 10
Female Junior 9
Male Sophomor 10
Female Junior 8
Male Sophomor 8
Female Senior 9
Female Senior 7.25
Female Sophomor 7.25
Male Sophomor 7.25
Female Freshman 23
Female Sophomor 10
Female Sophomor 9
Female Sophomor 10
Female Sophomor 12
Female Senior 9
Female Junior 7.5
Female Junior 10
Female Junior 9
Female Junior 11
Female Junior 9.5
Female Sophomor 8.1
Female Senior 10
Female Junior 8.5
Female Sophomor 10
Male Freshman 8.5
Female Senior 21
Female Freshman 9
Female Freshman 12
Female Sophomor 10
Male Senior 10
Female Junior 20
Male Sophomor 8.5
Male Senior 8.5
Male Junior 8.25
Female Sophomor 10
Male Junior 9.5
Female Sophomor 9
Male Junior 7.25
Male Senior 9.25
Female Senior 10
Female Senior 11
Female Sophomor 9
Male Senior 10
Female Sophomor 7.5
Female Junior 12
Female Sophomor 12
Male Junior 14.25
Female Sophomor 7.25
Female Freshman 10
Female Junior 10
Female Sophomor 10
Female Junior 20
Female Senior 9
Male Sophomor 11
Female Junior 7.75
Male Sophomor 8
Female Freshman 7.5
Female Senior 8
Female Junior 8.75
Male Freshman 8
Female Sophomor 8.5
Female Sophomor 8.25
Male Junior 9.25
Male Junior 18.5
Female Sophomor 8
Female Sophomor 8
Female Junior 8.78
Male Sophomor 8
Male Junior 10.71
Female Sophomor 7.25
Female Junior 9.25
Male Sophomor 8.5
Female Sophomor 10
Female Senior 15.25
Female Freshman 7.25
Male Junior 8.5
Male Sophomor 8
Female Junior 15
Female Junior 12
Female Sophomor 10
Male Sophomor 14.5
Male Junior 11
Female Sophomor 7.25
Male Junior 10
Female Sophomor 8
Female Sophomor 8.25
Female Senior 14
Female Sophomor 9.25
Male Freshman 7.25
Female Sophomor 4.5
Female Sophomor 8
Male Sophomor 9
Female Sophomor 7.25
Female Sophomor 15
Female Freshman 12
Female Sophomor 10
Female Senior 7.25
Female Senior 10.25
Female Junior 8
Male Junior 10
Male Senior 16
Female Sophomor 7.25
Female Sophomor 10.25
Male Sophomor 18
Male Junior 9.25
Male Junior 15
Female Freshman 7.25
Female Freshman 8
Female Junior 10
Female Freshman 11
Male Senior 9
Male Senior 10.25
Female Senior 10

1) A friend of yours suggests that at least 10% of people at your university have had something stolen from them on campus in the past year. This is your population value. You take a random sample of 100 people in you classes to determine if your friend is correct, you think that they may be wrong. You find that 15% of them have had something stolen.

Would you have a one or two tailed test?

Two Tailed

One tailed

2) What is the strength of the following correlation? -0.512

Moderate

Strong

Weak

3) A friend of yours suggests that at least 10% of people at your university have had something stolen from them on campus in the past year. This is your population value. You take a random sample of 100 people in you classes to determine if your friend is correct, you think that they may be wrong. You find that 15% of them have had something stolen.

Would you use z or t to test this hypothesis?

Z Distribution

T Distribution

find and provide three examples of data visualizations which mislead a viewer (at least one should be in the business context).

include the screenshots/pictures of those visualizations. Explain why they mislead.

Advertising expenditures and sales for the last 5 quarters have been as follows:

In quarter 3, a new product was introduced that would influence sales in quarter 3. 4 and 5. The following model is established:

y=β₁x₁+β₂x₂+ ε

where y=sales, x₁=advertising expenditures, x₂ is a variable that is 1 when the new product is available and 0 otherwise, and ε is an error component. Find the least squares estimate of β_1.