Assume that the mean SAT score of students admitted to Northeastern Illinois University is 1090. The members of the Psychology Department believe that students who decide to major in Psychology have higherSAT scores than the general population of students at the university. A sample of N= 10 newly declared Psychology majors consent to have their entrance records reviewed.

Their scores are as follows: 1276, 1248, 1066, 1106, 1138, 1215, 1168, 1185, 933, and 1425.Can the department conclude that Psychology majors have higher SAT scores than the university as a whole?

(a)Set up your hypotheses using the correct notation (1mark)

(b)Compute tobt(1.5marks)

(c)What is the statistical decision? JUSTIFY YOUR ANSWER (1mark)

(d)What is the conclusion? (1mark)

(e)Compute the 95% Confidence Interval for μ (1 mark)

The calculator at this link will allow you to perform a one-way chi-square or “goodness of fit test”: http://vassarstats.net/csfit.html. Fifty students can choose between four different professors to take Introductory Statistics. The number choosing each professor is shown below. Use the calculator above to test the null hypothesis that there is no preference for professors -- that there is an equal chance of choosing each of them. Report your results including chi-square, degrees of freedom, p-value and your interpretation. Use an alpha level of .05. Be careful not to over interpret – state only what the test result tells you.

Professor N

Dr. Able 20

Dr. Baker 8

Dr. Chavez 14

Dr. Davis 8

7.1.6

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the type I and type II errors in this case, consequences of each error type for this situation, and the appropriate alpha level to use.

After receiving your bachelor’s degree in personnel management, you were hired by a small but expanding life insurance company. Your first assignment is to develop a more efficient technique for the preliminary screening of applicants for sales positions. Since the firm employs only college graduates, you decide to work with information focusing on their performance during college. A random sample of 25 from the firm’s current sales force is selected and the following information is obtained:

Last year’s performance evaluation score

College grade point average (GPA)

Percent of total college expenses earned by the individual

Number of social organizations the individual belonged to

                                    Percent of       Number of

Performance               Expenses         Social

Score               GPA    Earned                        Organizations

43                    2.1       50                    2

47                    2.8       20                    5

53                    2.6       10                    3

56                    2.7       60                    1

57                    3.8       0                      0

64                    2.6       30                    2

68                    3.2       10                    1

68                    2.8       30                    2

74                    2.6       10                    2

75                    2.9       40                    1

77                    3.0       30                    0

78                    3.2       15                    1

81                    3.4       20                    2

83                    2.8       40                    3

87                    2.6       60                    5

88                    3.1       50                    0

89                    2.4       80                    4

90                    3.3       10                    2

91                    2.9       50                    6

92                    3.5       40                    1

93                    3.7       30                    2

94                    3.1       20                    5

95                    3.6       70                    1

96                    3.2       10                    4

97                    3.4       40                    0

On the basis of the data obtained, what recommendations can you make regarding the preliminary screening of applicants for sales positions?

Two buckets are lying on a table. Bucket #1 has five red and two yellow balls in it. Bucket #2 contains three red and four yellow balls. In all of the questions below, the buckets start with this composition.

a. Two balls are drawn at random from bucket #1. What is the probability that one is red and one is yellow?

b. One ball is drawn at random from bucket #1 and placed into bucket #2. One ball is then drawn from bucket #2. What is the probability that this ball is red?

c. Balls are drawn one by one from bucket #2 until a red ball is drawn. What is the probability that the first red ball is drawn on the third draw.

• What do you think is the biggest advantage of choosing a related-samples t-test over an independent-samples t-test? Why?
• What do you think is the biggest advantage of choosing an independent-samples t-test over a related-samples t-test? Why?
• Which test do you think is the most helpful when looking at relationships in psychology?

Using the below data, compare the average salary in 1999-2000 by region to 2014-15 by region. Which groups had statistically significant increases? Decreases? Please use excel to solve and show the steps.  

Average Salary by Region:

If u = 100, sigma = 12, and n = 16, then use the t distribution to evaluate the probability ? exceeds 103?

Express your answer as a percentage with 3 decimals

An engineer is concerned about the potential loss due to failures of equipment. He obtained the following information regarding the failure events:

There are two possible failure types F1 and F2, which are unrelated;

F1 occurs with 3% in 10 years probability;

F2 occurs with 7% in 15 years probability, and

Associated costs in case of failures for F1 and F2 are $1000 and $400, respectively.

(a) Which failure event (F1 or F2) is more likely to happen during a year of operation?

(b) What is the expected loss due to the failures F1 and F2 in a year?

(c) What is the probability of at least one failure in 5 years?

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 39% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 21 strikes. Find the following probabilities. (Round your answers to four decimal places.)

(a) 12 or fewer fish were caught

(b) 5 or more fish were caught

(c) between 5 and 12 fish were caught

Question 1)

For safety reasons, 4 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 4 systems detects theft with a probability of 0.82 independently of the others.

The bank, obviously, is interested in the probability that when a theft occurs, at least one of the 4 systems will detect it. What is the probability that when a theft occurs, at least one of the 4 systems will detect it?

Your answer should be rounded to 5 decimal places.

__________________________________________________________________________

Question 2

According to the information that comes with a certain prescription drug, when taking this drug, there is a 15% chance of experiencing nausea (N) and a 46% chance of experiencing decreased sexual drive (D). The information also states that there is a 10% chance of experiencing both side effects.

What is the probability of experiencing neither of the side effects?

Your answer should be to two decimal places.

_____________________________________________________________________________________________________________

Question 3

According to the information that comes with a certain prescription drug, when taking this drug, there is a 18% chance of experiencing nausea (N) and a 50% chance of experiencing decreased sexual drive (D). The information also states that there is a 11% chance of experiencing both side effects.

What is the probability of experiencing nausea or a decrease in sexual drive?

Your answer should be rounded to 2 decimal places.

______________________________________________________________________________________________

Question 4

An engineering school reports that 55% of its students are male (M), 39% of its students are between the ages of 18 and 20 (A), and that 34% are both male and between the ages of 18 and 20.

What is the probability of a random student being chosen who is a female and is not between the ages of 18 and 20?

Your answer should be to two decimal places.

_________________________________________________________________________________

Question 5

An engineering school reports that 53% of its students were male (M), 36% of its students were between the ages of 18 and 20 (A), and that 28% were both male and between the ages of 18 and 20.

What is the probability of choosing a random student who is a female or between the ages of 18 and 20? Assume P(F) = P(not M).

Your answer should be given to two decimal places.

______________________________________________________________________________________

Question 6

An engineering school reports that 54% of its students were male (M), 39% of its students were between the ages of 18 and 20 (A), and that 25% were both male and between the ages of 18 and 20.

What is the probability of a random student being male or between the ages of 18 and 20?

Your answer should be rounded to two decimal places.

_______________________________________________________________________________________________

Question 7

Let A and B be two independent events such that P(A) = 0.14 and P(B) = 0.76.

What is P(A or B)?

Your answer should be given to 4 decimal places.

_____________________________________________________________________________

Question 8

Let A and B be two independent events such that P(A) = 0.3 and P(B) = 0.6.

What is P(A and B)?

Your answer should be given to 2 decimal places.

_______________________________________

Question 9

Let A and B be two disjoint events such that P(A) = 0.24 and P(B) = 0.33.

What is P(A and B)?

____________________________________________________

Question 10

Let A and B be two disjoint events such that P(A) = 0.08 and P(B) = 0.54.

What is P(A or B)

__________________________________________________

Question 11

The following probabilities are based on data collected from U.S. adults. Individuals are placed into a weight category based on weight, height, gender and age.

Based on this data, what is the probability that a randomly selected U.S. adult weighs more than the healthy weight range?

Your answer should be given to 3 decimal places.

_______________________________________________________________________

Question 12

The probabilities for the amount that can be won on a lottery game are given in the table below. Find the missing probability X.

X =

____________________________________________________

For years, the drug Vioxx, developed and marketed by Merck, was one of the blockbuster drugs on the market. One of a number of so-called Cox-2 anti-inflammatory drugs, Vioxx was considered by many people a miracle drug for alleviating the pain from arthritis and other painful afflictions. Vioxx was marketed heavily on television, prescribed by most physicians, and used by an estimated two million Americans. All of that changed in October 2004, when the results of a large study were released. The study, which followed approximately 2600 subjects over a period of about 18 months, concluded that Vioxx use over a long period of time caused a significant increase in the risk of developing serious heart problems. Merck almost immediately pulled Vioxx from the American market and doctors stopped prescribing it. On the basis of the study, Merck faced not only public embarrassment but the prospect of huge financial losses.

More specifically, the study had 1287 patients use Vioxx for an 18 period, and it had another 1299 patients use a placebo over the same period. After 18 months, 45 of the Vioxx patients had developed serious heart problems, whereas only 25 patients on the placebo developed such problems.

*Given these results, would you agree with the conclusion that Viozz caused a significant increase in the risk of developing serious heart problems? First, answer this from a purely statistical point of significant means statistically significant. *What hypothesis should you test, and how should you run the test?

*When you run the test, what is the corresponding p-value? Next, look at it from the point of view of patients. *If you were a Vioxx user, would these results cause you significant worry? After all, some of the subjects who took placebos also developed heart problems, and 45 might not be considered that much larger than 25 . Finally, look at it from Merck’s point of view. *Are the results practically significant to the company?* What does it stand to lose? *Develop an estimate, no matter how wild it might be, of the financial losses Merck might incur. Just think of all of those American Vioxx users and what they might do.

In a survey regarding an upcoming presidential primary, 1000 people were asked whether or not they favor a particular candidate. 214 of the respondents indicated that they favor the candidate. Form a 95% confidence interval for the proportion of voters who favor the candidate.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5805 physicians in Colorado showed that 3035 provided at least some charity care (i.e., treated poor people at no cost).

(a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)

lower limit

upper limit

Part 2

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 64 professional actors, it was found that 40 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

lower limit

upper limit