STAT 211 EXAM 3 – FORM A FALL03

·  Possible critical values that may be needed are =1.28, =1.645, =1.96, =1.318, =1.711, =2.064, =12.401, =13.848, =15.659, =39.364, =36.415, =33.196

The width of a casing for a door is normally distributed with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23 inches and a standard deviation of 1/16 inches. Assume that the width of a casing door and the width of the door are independent. Answer the following 3 questions using this information.

  1. Which of the following is the expected value of the difference between the width of the casing and the width of the door?

(a)  1 E(X-Y)=E(X)-E(Y)=24-23=1

(b)  22

(c)  23

(d)  24

(e)  25

  1. Which of the following is the standard deviation of the difference between the width of the casing and the width of the door?

(a)  0.0117

(b)  0.0195

(c)  0.1083

(d)  0.1398

(e)  0.1791

  1. What is the probability that the difference between the width of the casing and the width of the door exceed 1/4 inch?

(a) 0

(b) 0.25

(c) 0.50

(d) 0.75

(e) 1 P(X-Y>0.25)==P(Z>-5.27)=1

Aircrew escape systems are powered by a solid propellant. The burning rate of this propellant is an important characteristic. Specifications require that the mean burning rate must be µ=50 cm/s. We know that the standard deviation of burning rate is s=2 cm/s. The experimenter selects a random sample of n=25 from a normal population and obtains a sample average burning rate of =51.3 cm/s. Answer the following 4 questions using this information.

  1. What should be the sample size to obtain the 95% confidence interval for the true mean burning rate with the interval width of 0.5?

(a)  8

(b)  16

(c)  62

(d)  246 n=

(e)  266

  1. Which of the following is the 95% confidence interval for the true mean burning rate?

(a)  (50.47 , 52.13)

(b)  (50.52 , 52.08) =

(c)  (50.56 , 52.05)

(d)  (50.60 , 52.01)

(e)  (50.65 , 51.96)

  1. Are the specifications for the true mean satisfied when you look at the 99% interval for the true mean burning rate, (50.27 , 52.33)?

(a)  Yes

(b)  No m=50 does not fall in between the interval limits

  1. When the experimenter selected the random sample of 25, he/she computed the standard deviation of burning rate, s=1.9 cm/s. Do the data confirm the known standard deviation when you compute the 95% confidence interval for the true standard deviation?

(a)  Yes s=2 falls in the 95% C.I for s: =(1.4836 , 2.6432)

(b)  No

  1. Which of the following is the area between 13.848 and 39.364 on the chi-square curve when the sample size is 25?

(a)  0.025

(b)  0.05

(c)  0.925 = 1-0.025-0.05 39.364 (13.838) gives you the area on the right (left) as 0.025 (0.05).

(d)  0.95

(e)  0.975

The weight of a small candy is normally distributed with a mean of 0.1 ounce and a standard deviation of 0.01 ounce. Suppose that random sample of 16 small candies are placed in a package. Answer the following 3 questions using this information.

  1. What is the expected value of package weight?

(a)  0.01

(b)  0.1

(c)  0.16

(d)  1.6 =

(e)  16

  1. What is the variance of package weight?

(a)  0.0016 =

(b)  0.016

(c)  0.16

(d)  1.6

(e)  16

  1. What is the probability that the average candy weight in the package is less than 0.1 ounce?

(a)  0

(b)  0.1

(c)  0.4

(d)  0.5 =

(e)  0.8

An industrial engineer’s assistant made 50 random observations of the upholstery installation team in an automobile assembly plant. During 12 of the observations the workers were arranging materials beside their workstation. Answer the following 3 questions using this information.

  1. Are the large sample conditions satisfied to construct the confidence interval for the true proportion of time installers spends arranging materials?

(a)  Yes 50(12/50)=12 ³ 10 and 50(38/50)=38 ³ 10

(b)  No

  1. Which of the following is the point estimate for the true proportion of time installers spend arranging materials?

(a)  1/5

(b)  1/12

(c)  1/50

(d)  5/50

(e)  12/50

  1. What sample size is required for the width of a 95% confidence interval for the true proportion of time installers spends arranging materials to be at most 0.10?

(a)  21

(b)  51

(c)  71

(d)  141

(e)  281 n==280.28

The U.S. Census Bureau produces estimates of total resident population for each state on an annual basis. The following is the descriptive statistics obtained by using MINITAB software.

Variable n Mean Median TrMean StDev SE Mean

X: # of Births 51 79366 54318 64220 93998 13162

Y: # of Deaths 51 47958 34066 41493 48872 6843

Variable Minimum Maximum Q1 Q3

X: # of Births 6035 529610 18942 85356

Y: # of Deaths 3142 234012 12831 57544

Answer the following 5 questions using this information.

  1. Which of the following is the point estimate for the true median of deaths?

(a)  34066 = sample median

(b)  47958

(c)  54318

(d)  79366

(e)  234012

  1. Which of the following is the MLE for the true standard deviation of deaths if the death data are normally distributed?

(a)  48390.49 =

(b)  48872

(c)  93071.89

(d)  93998

(e)  8662376475

  1. Assume deaths data are normally distributed. Is the MLE for the true variance of deaths its unbiased estimator?

(a) Yes

(b) No

  1. The 95% and the 99% confidence intervals for the true average number of births are computed below. Which of the following is the 99% confidence interval for the true average number of births?

(a)  (45472.94 , 113259.06) 99% is wider than 95%

(b)  (53567.79 , 105164.21)

  1. Which of the following is the estimated standard error for the difference between the average number of births and the average number of deaths?

(a)  14835.104 =

(b)  11243.431

(c)  80294.157

(d)  105943.836

  1. If the critical value is =0.72 in the two-sided confidence interval for the population mean, which of the following is the corresponding confidence level?

(a)  0.2358

(b)  0.5284 = P(Z<0.72)-P(Z<-0.72)=0.7642-0.2358

(c)  0.7642

(d)  0.8446