# 220_1_s_2000-2001

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:                   ‫أستاذ المادة‬                               ______________________________: ‫اسم الطالب‬
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: ‫رقم الشعبة أو وقتها‬                                              ______________________________: ‫رقم الطالب‬
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First Exam – QM 220 - Spring 2000/2001

[1] Answer the following questions by choosing the right answer or filling the spaces:
1) When samples are taken from a population with unknown standard deviation, then the sampling
distribution of the sample mean (i.e. x ) has a t distribution:
a) If n  30                                        c) If the population is normal
b) Always                                           d) If n  30

2) The                            significant                                    level                            ()                          is                       defined                                 as:
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3) The total area under the t-distribution is:
(a) Larger than the area under the normal                                                                                          (b) Less than the area under the normal
(c) The same as the normal                                                                                                         (d) cannot determine.

4) The confidence interval length of the population variance (  2 ) from a sample of size n will
when the sample variance (S) increases.
_____________________________________________________

5) Type                                   II                              error                                   is                             defined                                      as:
_____________________________________________________________________________________________________________________________ __________________________________________________

_____________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________

6) The direction of the rejection region in testing a hypothesis depends on:
(a) Ho                                              (b) 
(c) 1 -                                            (d) HA.

7) The size of the rejection region in testing a hypothesis is determined by:
(a) Ho                                               (b) 
(c) HA.                                              (d) None of the above

8) Testing a hypothesis can be done through an available confidence interval estimate:
(a) If the alternative hypothesis is greater than (b) If the alternative hypothesis is
less than
(c) If the alternative hypothesis is two-sided    (d) none of the above

9) To estimate the value of the population variance through confidence interval we use a test statistics
that has:
(b) a normal distribution                         (b) a t – distribution with n-1 D.F.
(c) a chi-square (  ) distribution with n-1 D.F.
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(d) an unknown distribution

10) Any mathematical formula that can be used as a Test Statistics should have the following
conditions:

( )       _________________________________________________________________________________________________________________________________________________________________________________________________________________________________

( )       _________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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( )   _________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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[2]   A machine is used to fill a package of 200 grams of black pepper. The net weight of these
packages has a normal distribution with mean equal 200 grams and a variance of 16 grams2.

a) What percentage of packages contains less than 195 grams:

b) What is the net weight of a black pepper package so that 10% of all packages
have net weight more that it.

[3] A manufacturing factory produces detergent. To estimate the mean amount of detergent filled in
a 1-liter bottle using a confidence interval with 0.99 significant level. The company knows that
the amount of detergent in 1 liter bottle follows the normal distribution with standard deviation
equals 0.060 liter. What is the sample size needed such that the estimate is with in 0.015 liter of
the population mean (i.e.  0.015 from ).

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[4]A software company claims that a program they recently introduced in the market would take the
average user with computer experience 6 hours to learn. To test this claim a sample of 12 persons
with computer experience was chosen at random. The following is the time in hours each has taken
to learn the program:
6.15 6.25 5.80 6.20 7.25 6.60 6.75 5.50 5.90 6.40 6.25 5.75
If it is known that the time it takes to learn the program follows the normal distribution with
mean  and standard deviation . The data were fed to MINITAB and analyzed to produce the
following results:

Test of mu = 6      vs     mu > 6
Variable           N         Mean         StDev      SE Mean          T         P
C1                12        6.233         0.481        0.139        1.68      0.060

(a) What are the hypotheses:

(b) Write the form of the TEST Statistics? It’s distribution? And find it’s value?

(c) Specify the rejection and non-rejection (acceptance) regions at =0.01? (Draw them)

(d) State your conclusion regarding the null hypothesis?

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[5] For the same data in the previous question (4) if it is known that the true value of the population
variance is 0.20 hour2. Test the claim of the Software Company using the same previous sample
and 90% significant level against an alternative hypothesis that claims that the required time to
learn the program is more than 6 hours.

(a) What are the hypotheses:

(b) Write the form of the TEST Statistics? It’s distribution? And find it’s value?

(c) specify the rejection and non-rejection (acceptance) regions at =0.10? (draw it)

(d) State your conclusion regarding the null hypothesis?

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