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KING FAHD UNIVERSITY OF PETROLEUM & MINERALS

DEPARTMENT OF MATHEMATICAL SCIENCES

DHAHRAN, SAUDI ARABIA

STAT 201: STATISTICAL METHODS

Final Exam, Semester 052

Time: 7.0 pm- 9.3 pm., Saturday 3/6/ 2006

Instructors: Prof. Hassen A. Muttlak

Surname: ID#

Question No

Full Marks

Marks Obtained

1.  (4 + 4 + 4 + 4= 16 points ) The following values represent the presents measurements of various properties of shallow water in certain aquifer system. Following are measurements of electrical conductivity (in microsiements per centimeter) for 14 water samples.

375, 424, 489, 410, 522, 313, 488, 230, 365, 488, 575, 540, 461, 620

i)  Calculate the mean, median, mode and 25th percentile of the data.

ii)  Calculate the range and the standard deviation.

iii)  Draw a stem and leaf diagram and comment on the shape of graph.

iv)  Is the empirical rule satisfy? Explain.

2.  ( 5+ 5+ 3 + 2 + 5 = 20 points) For the data in question 1

i)  Construct a 95% confidence interval for the true population mean and interpret your confidence interval.

ii)  The researcher believes that the average measurements of shallow water should be more than 400. Use 5% level of significance to test the researcher claim.

iii)  What are the assumptions that you need to answer the above two parts.

iv)  Based on your answer in question 1, do you think that your assumptions in part (iii) is valid? Explain.

v)  Suppose that the data in question 1 represent an elementary sample, the researcher wish to estimate the population mean to be with in ± 30 with 90% confidence, determine the sample size required.

3.  (5 +5+5=15) In a survey by news paper found that 329 out of 763 adults said they would travel to outer space in their lifetime, given the chance.

i)  Estimate the true proportion of adults who would like to travel to outer space with 92% confidence.

ii)  The people who conducted the survey believe that less than 45% of the adults would like to travels outer space. Use 5% level of significance and the p-value method to test this claim.

iii)  Find the maximum sample size to estimate the true proportion of adults who would like to travel outer space to be within 4% and with 95% confident.

4.  (13 points) A high school is interested in determining whether two of its instructors are equally able to prepare students for countrywide examination in mathematics. Seventy two students taking mathematics this semester were randomly divided into two groups of 36 each. Instructor 1 taught mathematics to first group, and instructor 2 to the second. At the end of semester, the students took the countrywide examination, the following results:

Can you conclude from these results that the instructors are not equally able in preparing students for the examination? Use 5% level of significance. Clearly state your hypotheses, test statistic, assumptions and final conclusions.

(5+5+5+5=20 points) The following are measurements of the air velocity (x) ( cm/ sec) and evaporation coefficient (y) () of burning fuel droplets in an impulse engine:

You may use any of the following information

,

i)  Fit the linear regression line to predict the evaporation coefficient if the air velocity is 330.

ii)  Does a linear relationship exist between the air velocity and evaporation coefficient? Use 5% level of significance.

iii)  Find 95% confidence interval for the evaporation coefficient with 330 cm/ sec air velocity.

iv)  Find the coefficient of determination and the correlation coefficient and interpret both of them

.

5.  Answer any four of the following for 4 points each.

i)  The probability that Ali will accepted by the college of his choice and obtain scholarship is 0.35. If the probability that he accepted by the college is 0.65, find the probability he will obtain a scholarship given that he is accepted by the college.

ii)  A pizza shop owner determines that the number of pizzas that delivered each day. Find the mean and standard deviation for the distribution shown.

iii)  If 80% of the people in a community have Internet access from their homes, for a sample of 6 people, find the probability at most 2 have internet access.

iv)  The national average SAT score is 1019. If we assume a normal distribution with s =90, what is the probability that a randomly selected score exceeds 1200? What is the 90th percentile score?

v)  The average electric bill in a city is SR270 for the month of March. The standard deviation SR24. What is the probability that the sample mean of 36 bills will be less than SR260?