Stat 202 midterms 100% correct answers (with detailed excel

 
   

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1.The MPG (miles per gallon) for a certain compact car is normally distributed with a mean of 31 and a standard deviation of 0.8. What is the probability that the MPG for a randomly selected compact car would be less than 32?

                0.5596

                0.3944

                0.8944

                0.1056

2.In a simple regression, there are n – 2 degrees of freedom associated with the error sum of squares (SSE).

                True

                False

3.A researcher’s results are shown below using Femlab (labor force participation rate among females) to try to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states.

 

 Source of variation         df            SS           MS         F

Regression          1              5377.836              5377.836              5.228879

Residual               48           49367.389            1028.487             

Total      49           54745.225                           

 

 

What is the R2 for this regression?

                .1605

                .0982

                .9018

                .8395

 [The following information applies to the questions displayed below.]

 

 

The sodium content of a popular sports drink is listed as 204 mg in a 32-oz bottle. Analysis of 14 bottles indicates a sample mean of 210.5 mg with a sample standard deviation of 24.2 mg.

 

 

 4.(a)     

State the hypotheses for a two-tailed test of the claimed sodium content.

                H0: µ ≤ 204 vs. H1: µ > 204

                H0: µ = 204 vs. H1: µ ≠ 204

                H0: µ ≥ 204 vs. H1: µ < 204

 

 5.

(b)         

Calculate the t test statistic to test the manufacturer’s claim. (Round your answer to 4 decimal places.)

 

  Test statistic      

 

 

 6.

(c)

At the 1 percent level of significance (α = 0.01) does the sample contradict the manufacturer’s claim?

                 

                  

H0. The sample

the manufacturer’s claim.

 

 

 7.

(d-1)     

 

Use Excel to find the p-value and compare it to the level of significance. (Round your answer to 4 decimal places.)

                 

                  The p-value is . It is

than the significance level 0.01.

                 

(d-2)      Did you come to the same conclusion as you did in part (c)?

                 

               

                Yes

                No

8.A charity raffle prize is $1,000. The charity sells 4,000 raffle tickets. One winner will be selected at random. At what ticket price would a ticket buyer expect to break even?

                $0.25

                $0.50

                $0.75

                $1.00

9.At Joe’s Restaurant, 80 percent of the diners are new customers (N), while 20 percent are returning customers (R). Fifty percent of the new customers pay by credit card, compared with 70 percent of the regular customers. If a customer pays by credit card, what is the probability that the customer is a new customer?

                .7407

                .5000

                .5400

                .8000

10.Within a given population, 22 percent of the people are smokers, 57 percent of the people are males, and 12 percent are males who smoke. If a person is chosen at random from the population, what is the probability that the selected person is either a male or a smoker?

                .67

                .22

                .43

                .79

11.A fair die is rolled. If it comes up 1 or 2 you win $2. If it comes up 3, 4, 5, or 6 you lose $1. Find the expected winnings.

                $1.00

                $0.50

                $0.00

                $0.25

12.Assume that X is normally distributed with a mean μ = $64. Given that P(X ≥ $75) = 0.2981, we can calculate that the standard deviation of X is approximately:

                $13.17.

                $5.83.

                $7.05.

                $20.76.

13.If the attendance at a baseball game is to be predicted by the equation Attendance = 16,500 – 75 Temperature, what would be the predicted attendance if Temperature is 90 degrees?

                9,750

                6,750

                10, 020

                12,250

 [The following information applies to the questions displayed below.]

 

A random sample of 140 items is drawn from a population whose standard deviation is known to be σ = 50. The sample mean is x = 780.

 

 

 14.

(a)         

Construct an interval estimate for μ with 98 percent confidence. (Round your answers to 4 decimal places.)

 

 

 

  The 98 percent confidence interval is from         to . 

 

 

 

 15.

(b)         

 

Construct an interval estimate for μ with 98 percent confidence, assuming that σ = 100. (Round your answers to 4 decimal places.)

 

  The 98 percent confidence interval is from         to .

 

 

 16.

(c)          

 

Construct an interval estimate for μ with 98 percent confidence, assuming that σ = 200. (Round your answers to 4 decimal places.)

 

  The 98 percent confidence interval is from         to .

 

 

 17.

(d)          Describe how the confidence interval changes as σ increases.

                The interval stays the same as σ increases.

                The interval gets wider as σ increases.

                The interval gets narrower as σ increases.

                The interval gets wider as σ decreases.

18.What are the mean and standard deviation for the standard normal distribution?

                μ = 0, σ = 1

                μ = 0, σ = 0

                μ = 1, σ = 0

                μ = 1, σ = 1

19.A negative value for the correlation coefficient (r) implies a negative value for the slope (b1).

                True

                False

20.The Poisson distribution has only one parameter.

                True

                False

21.Find the probability that either event A or B occurs if the chance of A occurring is .5, the chance of B occurring is .3, and events A and B are independent.

                .15

                .80

                .65

                .85

22.The total sum of squares (SST) will never exceed the regression sum of squares (SSR).

                True

                False

23.A prediction interval for Y is narrower than the corresponding confidence interval for the mean of Y.

                True

                False

24.A biometric security device using fingerprints erroneously refuses to admit 2 in 1,400 authorized persons from a facility containing classified information. The device will erroneously admit 2 in 1,004,000 unauthorized persons. Assume that 95 percent of those who seek access are authorized.

 

If the alarm goes off and a person is refused admission, what is the probability that the person was really authorized? (Round your answer to 5 decimal places.)

 

  Probability         

25.The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 534 MPa with a standard deviation of 13 MPa.

 

(a)         

 

What is the probability that a randomly chosen sample of glass will break at less than 534 MPa? (Round your answer to 2 decimal places.)

 

  Probability         

 

(b)         

 

What is the probability that a randomly chosen sample of glass will break at more than 559 Mpa? (Round your answer to 4 decimal places.)

 

  Probability         

 

(c)          

 

What is the probability that a randomly chosen sample of glass will break at less than 567 MPa? (Round your answer to 4 decimal places.)

 

  Probability

                 

26.Half of a set of the parts are manufactured by machine A and half by machine B. Five percent of all the parts are defective. Two percent of the parts manufactured on machine A are defective.

 

Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.)

 

  Probability       

 

27.A student’s grade on an examination was transformed to a z value of 0.67. Assuming a normal distribution, we know that she scored approximately in the top:

                25 percent.

                40 percent.

                50 percent.

                15 percent.

28.Which pairs of events are independent?

  

(a)          P(A) = 0.28, P(B) = 0.14, P(A∩B) = 0.10.

                 

                  A and B are

.

  

(b)          P(A) = 0.15, P(B) = 0.48, P(A∩B) = 0.05.

                 

                  A and B are

.

  

(c)           P(A) = 0.80, P(B) = 0.10, P(A∩B) = 0.08.

                 

                  A and B are

.

29.A large number of applicants for admission to graduate study in business are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. The top 2.5 percent of the applicants would have a score of at least (choose the nearest integer):

                646.

                617.

                606.

                600.

30.A random variable X is best described by a continuous uniform distribution from 20 to 45 inclusive. The mean of this distribution is:

                33.5.

                32.5.

                31.5.

                30.5.