Suppose you know that the amount of time it takes your friend Susan to get from her residence to class averages  50 minutes, with a standard deviation of 55 minutes. What proportion of Susan's trips to class would take more than  50 minutes? . Enter your answers accurate to two decimal places.

What proportion of her class would take more than  50 minutes?

What proportion of Susan's trips to class would take less than 40 minutes?

What proportion of Susan's trips to class would take more than  50 minutes or less than  40 minutes?

2. A new chemotherapy drug is released to treat leukemia and researchers suspect that the drug may have fewer side effects than the most commonly used drug to treat leukemia. The two drugs have equivalent efficacy. In order to determine if a larger study should be conducted to look into the prevalence of side effects for the two drugs, set up a Mann-Whitney U test at the alpha equals .05 level and interpret its results.

                        Number of Reported Side-Effects

Old Drug           0          1          3          3          5

New Drug          0          0          1          2          4

A) We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 16.5 is greater than the critical U value of 2.

B) We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 8.5 is greater than the critical U value of 2.

C) We reject H₀ in favor of H₁, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 16.5 is greater than the critical U value of 2.

D) We reject H₀ in favor of H₁, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 8.5 is greater than the critical U value of 2.

Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

1. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.
   
   Compute b₀ and b₁ (to 2 decimals).
   b₁
   b₀
   
   Complete the estimated regression equation (to 2 decimals).
   =  +  x
   
2. Compute the following (to 1 decimal):

   SSE
   SST
   SSR
   MSE

   
   
3. What is the coefficient of determination (to 3 decimals)? Note: report r² between 0 and 1.
   
   
   Does the estimated regression equation provide a good fit?
   SelectYes, it even provides an excellent fitYes, it provides a good fitNo, it does not provide a good fitItem 10
   
4. Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
   (  ,  )
   
5. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
   (  ,  )

The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenueproducing investments together with annual rates of return are as follows:

The credit union will have $2.4 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments.

• Risk-free securities may not exceed 30% of the total funds available for investment.
• Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).
• Furniture loans plus other secured loans may not exceed the automobile loans.
• Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.

How should the $2.4 million be allocated to each of the loan/investment alternatives to maximize total annual return? Round your answers to the nearest dollar.

What is the projected total annual return? Round your answer to the nearest dollar.

$  

A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 24 newly graduated law students. Their scores give a sample standard deviation of 63points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60.

(a) Find a 99% confidence interval for the population variance. (Round your answers to two decimal places.)

(b) Find a 99% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ² = 5.1. Suppose a recent study of age at first marriage for a random sample of 31 women in rural Quebec gave a sample variance s² = 2.9. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance.

(a) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

Do students reduce study time in classes where they achieve a higher midterm score? In a Journal of Economic Education article (Winter 2005), Gregory Krohn and Catherine O’Connor studied student effort and performance in a class over a semester. In an intermediate macroeconomics course, they found that “students respond to higher midterm scores by reducing the number of hours they subsequently allocate to studying for the course.” Suppose that a random sample of n = 8 students who performed well on the midterm exam was taken and weekly study times before and after the exam were compared. The resulting data are given in Table 10.6. Assume that the population of all possible paired differences is normally distributed.

Table 10.6

Paired T-Test and CI: Study Before, Study After

95% CI for mean difference: (3.73660, 12.51340)

T-Test of mean difference = 0 (vs not = 0): T-Value = 4.38, P-Value = .0032

(a) Set up the null and alternative hypotheses to test whether there is a difference in the true mean study time before and after the midterm exam.

H₀: µ_d =  versus H_a: µ_d ?

(b) Above we present the MINITAB output for the paired differences test. Use the output and critical values to test the hypotheses at the .10, .05, and .01 level of significance. Has the true mean study time changed?(Round your answer to 2 decimal places.)

t =   We have (Click to select)strongvery strongextremely strongno evidence.

(c) Use the p-value to test the hypotheses at the .10, .05, and .01 level of significance. How much evidence is there against the null hypothesis?

There is (Click to select)no evidencevery strong evidencestrong evidenceextermly strong evidence against the null hypothesis.

Measurements were recorded for the slapshot speed of 100 minor-league hockey players. These measurements were found to be normally distributed with mean of 84.388 mph and standard deviation of 3.3706 mph. Would it be unusual to record a value above 94.6 mph?

Question 6 options:

According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0499 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 337 independent returns from this year, what is the probability that at least 26 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Question 7 options:

According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0362 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 385 independent returns from this year, what is the probability that less than 9 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Question 9 options:

2. Alice and 10 other users are sending packets using the pure ALOHA protocol. The duration of a packet is 40 msec. Each user sends a packet (including both originals and retransmissions) following a Poisson process with rate 1/400 packets/msec.

1. (a) What is the chance of success on Alice’ first attempt? (hint: the probability that there is no othertransmission within the vulnerable period of Alice’s attempt)

2. (b) What is the probability that Alice gets exactly k collisions and then a success? (hint: consider a Bernoulli trials process)

3. (c) What is the expected number of transmission attempts needed to successfully send a packet?

True or False:

13. A classical probability measure is a probability assessment that is based on relative frequency.

14. The probability of an event is the product of the probabilities of the sample space outcomes that correspond to the event.

15. If events A and B are independent, then P(A|B) is always equal to P(A).

16. Events that have no sample space outcomes in common and, therefore cannot occur simultaneously are referred to as mutually independent events.
17. The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and the probability of success changes from trial to trial.
18. The standard deviation of a binomial distribution is np(1-p).

19. In a binomial distribution the random variable X is discrete.

20. The standard deviation and mean are the same for the standard normal distribution.

21. In a statistical study, the random variable X = 1, if the house is colonial and X = 0 if the house is not colonial, then it can be stated that the random variable is continuous.

22. For a continuous distribution, P(X ≤ 10) is the same as P(X<10).

23. For a continuous distribution, the exact probability of any particular value is always zero.

24. For a binomial probability experiment, with n = 60 and p =.2, it is appropriate to use the normal approximation to the binomial distribution without continuity correction.

25. All continuous random variables are normally distributed.

5. (Casella & Berger, 2nd ed.) A p.d.f. is defined by f(x, y) = C(x + 2y) for 0 < y < 1 and 0 < x < 2, and is zero otherwise. a) Find the value of C. b) Are X and Y independent? c) Find the marginal p.d.f of X. d. Find the conditional p.d.f fy|x(y|x). e) Find E[Y |x = 1].

(1) According to the American Lung Association, 90% of adult smokers started smoking before turning
21 years old. Ten smokers 21 years old or older were randomly selected, and the number of smokers
who started smoking before 21 is recorded.
(a) State the distribution of the random variable of number of smoker of these 10 who started
smoking before age 21 and its two parameters.
(b) Find the probability that exactly 8 of them started smoking before 21 years of age. Do not
use statistical features of your calculator.
(c) Find the probability that fewer than 8 of them started smoking before 21 years of age.
(d) Find the probability that between 7 and 9 of them, inclusively, started smoking before 21 years
of age.
(e) Compute and interpret the mean of this random variable.
(f) Compute the standard deviation of this random variable.

Your patient’s mammogram is positive for breast cancer which has a fairly low rate in your state of 1 case per 1,000 women annually. You know from the literature that the mammogram test has a sensitivity of around 92% and a specificity of 95% depending on the study. What do you tell your patient when she asks do I have breast cancer.

Show your work in both a contingency table and using the shortcut Bayes Theorem.

For staffing purposes, a retail store manager would like to standardize the number of checkout lanes to keep open on a particular shift. She believes that if the standard deviation of the hourly customer arrival rates is 9 customers or less, then a fixed number of checkout lanes can be staffed without excessive customer waiting time or excessive clerk idle time. However, before determining how many checkout lanes (and thus clerks) to use, she must verify that the standard deviation of the arrival rates does not exceed 9. Accordingly, a sample of 25 hourly customer arrival rates was compiled for that shift over the past week.

a. Select the hypotheses to test whether the standard deviation of the customer arrival rates exceeds 9.

• H₀: σ² ≤ 81; H_A: σ² > 81

• H₀: σ² = 81; H_A: σ² ≠ 81

• H₀: σ² ≥ 81; H_A: σ² < 81

b. Calculate the value of the test statistic. Assume that customer arrival rates are normally distributed. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test Statistic: ???

Your leader wants you to evaluate the difference in cycle time between three different offices. Describe the steps you would take in the evaluation in order to provide a report so the leader can take action. In replies to peers, indicate whether you agree or disagree with the steps they outlined. Justify your response using what you learned from the topic materials

Because some people are unable to stand to have their height measured, doctors use the height from the floor to the knee to approximate their patients’ height (in cm).

a. Use Excel to determine the correlation coefficient of this data

b. Use Excel to determine the regression equation of this data

c. Find the overall height from a knee height of 45.3 cm

d. Find the overall height from a knee height of 52.7 cm

Choose one • 20 points

• a. r = 0.73220213

  b. Equation: y = 2.0217x + 67.746

  c. 159.32901

  d. 174.28959

• a. r = 0.82544241

  b. Equation: y = 2.5109x + 40.79

  c. 154.53377

  d. 173.11443

• a. r = 0.53611996

  b. Equation: y = 2.0217x + 67.746

  c. 159.32901

  d. 174.28959

• a. r = 0.908553861

  b. Equation: y = 2.5109x + 40.79

  c. 154.53377

  d. 173.11443