The finance director at Ubuntu University of Science and Technology is concerned about the overhead costs at her university. Cost pressures are severe and so controlling and reducing overheads is very important. The director believes overhead costs incurred are generally a function of the number of different academic programmes, and the number of enrolled students. The following data has since been collected for analysis:

Required

a) Using the above data, estimate the regression line

. b) Calculate the coefficient of determination.

c) What insights do the analyses provide about controlling and reducing overhead costs at the university?

1. A national car rental company is interested in determining whether the mean days that customers rent cars is the same between three of its major cities. The following data reflect the number of days people rented a car for a sample of people in each of three cities.

Nizwa Sohar Muscat

5 7 7

3 7 5

7 11 8

1 5 11

2 7 15

9 3 17

a. Write down the null and alternative hypotheses to be tested.

b. Construct the ANOVA table

. c. Given the value of the tabulated F = 3.68 (α=.05), test the hypotheses you formulated in ‘a’ above.

d. Clearly state the test’s decision and conclusion. e. Perform pairwise comparisons and make conclusions (using t = 1.5).

In what follows use any of the following tests/procedures: Regression, multiple regression, confidence intervals, one sided T-test or two sided T-test. All the procedures should be done with 5% P-value or 95% confidence interval.Some answers are approximated, choose the most appropriate answer.Open Brains data. SETUP: Scientists speculate that the heavier body the larger the human brain (Volume). Given the data your job is to confirm or disprove this assertion.

I. What test/procedure did you perform? (6.66 points)

• a. One sided T-test
• b. Two sided T-test
• c. Regression
• d. Confidence interval

II. Statistical interpretation? (6.66 points)

• a. Since P-value is small we are confident that the slope is not zero.
• b. Since P-value is small we are confident that the averages are different.
• c. Since P-value is too large the test is inconclusive.
• d. None of these.

III. Conclusion? (6.66 points)

• a. Yes, we can confirm the assertion.
• b. No, we cannot confirm the assertion.

  CCMIDSA: Corpus Collasum Surface Area (cm2)     FIQ: Full-Scale IQ      HC: Head Circumference (cm)     ORDER: Birth Order      PAIR: Pair ID (Genotype)        SEX: Sex (1=Male 2=Female)      TOTSA: Total Surface Area (cm2) TOTVOL: Total Brain Volume (cm3)        WEIGHT: Body Weight (kg)
  8.42    96      57.2    1       6       1       1806.31 1079    61.236
  7.44    88      57.2    1       7       1       2018.92 1104    79.38
  6.84    85      57.2    1       8       1       2154.67 1439    99.792
  6.48    97      57.2    1       9       1       1767.56 1029    81.648
  6.43    124     58.5    1       10      1       1971.63 1160    72.576
  7.62    101     57.2    2       6       1       1689.6  1173    61.236
  6.03    93      57.2    2       7       1       2136.37 1067    83.916
  6.59    94      55.8    2       8       1       1966.81 1347    97.524
  7.52    114     56.5    2       9       1       1827.92 1100    88.452
  7.67    113     59.2    2       10      1       1773.83 1204    79.38
  6.08    96      54.7    1       1       2       1913.88 1005    57.607
  5.73    87      53      1       2       2       1902.36 1035    64.184
  6.22    101     57.8    1       3       2       2264.25 1281    63.958
  5.8     103     56.6    1       4       2       1866.99 1051    133.358
  7.99    127     53.1    1       5       2       1743.04 1034    62.143
  7.99    89      54.2    2       1       2       1684.89 963     58.968
  8.76    87      52.9    2       2       2       1860.24 1027    58.514
  6.32    103     56.9    2       3       2       2216.4  1272    61.69
  6.32    96      55.3    2       4       2       1850.64 1079    107.503
  7.6     126     54.8    2       5       2       1709.3  1070    83.009

A total of n different products will be ordered from m different suppliers,

i) Find the probability that a given supplier will receive exactly k orders

ii) Find the probability that one of the suppliers will receive two thirds of the orders.

Question 1
“PhysicalFun” is a physical center which opens 24 hours per day. Each member of “PhysicalFun” has an access card. Members would be charged in a weekly basic (Sunday 12:00a.m. to Saturday 11: 59 p.m.) according to the accumulated number of hours of facilities used within a week. The weekly basic charge is $150 with an additional charge of $30 per hour. According to the company record, the number of hours a member spends in “PhysicalFun” in a week is normally distributed with mean 15 hours and standard deviation 2.8 hours.

1. (a) What are the average and standard deviation of weekly charge of a member?

2. (b) Suppose the middle 85% of weekly charge of a member is denoted by $(L1, L2). Find the values of L1

   and L2.

3. (c) The senior management suggests fixing the weekly charge per member at $700. Assume the number

   of hours a member spends in “PhysicalFun” would not be changed due to the change of the weekly charge

   calculation method. What proportion of members would pay more money than the original system?

4. (d) How many hours does a member spend in “PhysicalFun” in a week so he / she would be beneficial by

   the new system?

In your own words, Differentiate the following statistical terminology with some examples.

a. Population parameter and Sample Statistic.

b. Descriptive Statistic and inferential Statistic.

C. Nominal Scale and Ordinal Scale

d. Primary Data Source and Secondary Data Sources.

2. Data showing the population by state in million of people follow ( The World Almanac, 2012) The dataset in Excel file 2012Population.XLsx.

a. Develop a frequency distribution, a percent frequency distribution, and a histogram Use a class width of 2.5 million.

b. Does there appear to be any skewness in the distribution? Explain

c. What observation can you nake about the population of the 50 states?

Does living together cause divorce? Couples were given a standardized psychological assessment that indicates the likelihood of divorce (higher scores indicate a higher likelihood of divorce) and asked them how many months they've lived together. The data is reported below:

Please complete all steps of hypothesis testing, create a scatterplot, and write a short explanation for what you think may be the underlying factor in this correlation (hint: be careful not to associate causal factors).

Data for a sample of 30 apartments in a particular neighborhood are provided in the worksheet. You want to see if there is a direct relationship between Size of the Apartment and Rent.

Please see Attached Excel for Data.

Base on your results, If the Size of your Apartment increased by 1 Sq. Ft., on average, the Rent would increase by approximately how much?  

Place your answer, rounded to 2 decimal places, in the blank. Do not use any stray punctuation marks or a dollar sign. Make sure you put the 0 in front of the decimal.

For example, 34.56 would be a legitimate entry.   

The following data give the number of hours 10 students spent studying and their corresponding grades on their midterm exams.

A. Calculate the sum of squared errors (SSE). Use the values b0=61.3521 and b1=4.1338 for the calculations. Round your answer to three decimal places.

B. Calculate the estimated variance of errors, s2e. Round your answer to three decimal places.

C. Calculate the estimated variance of slope, s2b1. Round your answer to three decimal places.

D. Construct the 80%confidence interval for the slope. Round your answers to three decimal places. Lower endpoint: _______ Upper endpoint: ________

E. Construct the 98%confidence interval for the slope. Round your answers to three decimal places. Lower endpoint: _______ Upper endpoint: ________

Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 5 items sold through an auction.

A. Calculate the sum of squared errors (SSE). Use the values b0=4.5256b0=4.5256 and b1=0.0840b1=0.0840 for the calculations. Round your answer to three decimal places.\

B. Calculate the estimated variance of errors, s2e. Round your answer to three decimal places.

C. Calculate the estimated variance of slope, s2b1. Round your answer to three decimal places.

D. Construct the 90%confidence interval for the slope. Round your answers to three decimal places. Lower endpoint: ____ Upper endpoint: ________

E. Construct the 95%confidence interval for the slope. Round your answers to three decimal places. Lower endpoint: ____ Upper endpoint: ________

Consider the following experiment: Simultaneously toss a fair coin and, independently, roll a fair die.

1. Write out the 12 outcomes that comprise the sample space for this experiment.

2. Let X be a random variable that takes the value of 1 if the coin shows “heads” and the value of 0 if the coin shows “tails”. Let Y be a random variable that takes the value of the “up” face of the tossed die. And let Z = X + Y. Construct the probability mass function for Z.

3. Find the mean for Z.

4. Find the variance for Z.

An iceberg consists of frozen freshwater that has broken away from a glacier, and could be more than 15,000 years old. Icebergs in the Grand Banks area are estimated to weigh between 100,000 and 200,000 tons. Suppose a team of scientists aboard a research vessel operating in the Grand Banks area selects a random sample of 49 icebergs. The height is carefully measured for each, and the sample mean is x = 101 meters. Assume σ = 25 meters.

(a) Find a 99% confidence interval for the mean height of icebergs in the Grand Banks area (in meters). (Round your answers to four decimal places.)

(____________ , __________)meters

Given two independent uniform random variables U1 and U2 both with parameters [0,1],

1) Calculate the probability that 0.3 <= X + Y <= 0.8

2) Calculate the PDF of X+Y

3) Calculate the PDF of X-Y

In a college algebra class there are 18 freshman and 17 sophomores. Eight of freshman are females and 13 of sophomores are male. Student is selected at random, probability of selecting a female?

Three cards are drawn from a deck without replacement, what is the probability of selecting a king, a nine and a ten?

A light bulb is advertised as lasting a 100 hours with a standard deviation of 1500 hours. Find the probability of buying a light bulb and it lasting a) less than 1250 hours , b) between 901 and 1000 hours c) more than 901 hours

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