STAT20028 : Statistics For Analytical Decisions - Statistical Problem - Frequency Polygon Assignment Help

Statistics For Analytical Decisiond Assignment Help

TASK1 1. Classify each of the following scenarios as a statistical problem in either descriptive statistics or statistical The International Union for Conservation of Nature and Natural Resources (IUCN) provides a list of threatened species for various years and their categories. In 2000 the number of threatened species was 11,046 and in 2007 it was 16,306. Research by CQ University revealed that changing the brand name from the old ‘Central Queensland University’ to the current name is likely to attract mor Identify the following data to be nominal, ordinal, interval or

• The price of a house sold in Sydney in auction.Answer: Ratio. The zero price has a
• The income of employees in categories of low, middle, high and very  high.

2. The distance in kilometres travelled per litre by a random selection of cars is given in the table below

• Construct the frequency distribution using “5.0 to less than 9.0” as the first class
• Draw a histogram
• Draw a frequency polygon. The frequency polygon and the histogram must be on the same
• Draw an ogive and identify the median value in the ogive.

3.  A sample of returns from two portfolios (in percent) is given below: Find the mean value and standard deviation of returns for each of the portfolios Find the correlation coefficient of returns between the portfolios. Which portfolio is preferable?Why? 4.  A simple random sample survey of the employees of a large corporation yielded the accompanying table. If a person is chosen randomly in the corporation, then based on the table, answer the following (Provide answers as fractions. No need to give answers in decimal values):

• What is the probability that the person has Bachelor degree as the highest academicqualification?
• What is the probability that the person’s income level is Low given that he/she has a PhDdegree?
• What is the probability that the person has High or Very high incomelevel?
• Is the probability of a person’s income independent of his/her highest academic qualification?

TASK2 1.

• There are 4 books on mathematics, 3 books on chemistry and 5 books on literature in a book shelf. In how many ways the books can be arranged such that all mathematics books are together, all chemistry books are together and all literature books aretogether?
• Forest, an investor in the Australian Stock Exchange (ASX), prepares a portfolio consisting of ten stocks. He believes, due to global financial crisis, the probability that the price of any one stock will decrease is 0.30 and the price movements of the stocks areindependent.
• What is the probability that none of his stocks willdecline?
• The number of accidents that occur at a traffic intersection has a Poisson distribution with an average rate of 2 accidents per What is the probability that there willbe
  • between 2 and 3 (inclusive) traffic accidents at that intersection next year?
  • less than 2 traffic accidents next year?
• The time of arrival of a person at work has a uniform distribution from 8:40am to 9:20am. On any day, what is the probability that the person will not arrive in the office early given that office starts from 9:00am?
• Women aged 60 to 69 are, of course, not young adults.  The mean BMD  in this age group is -1.2 (negative two) on the scale for young adults. Suppose that the standard deviation is the same as for young adults. What percent of this older population hasosteoporosis?
• Osteoporosis is a condition in which the bones become brittle due to loss of minerals. To diagnose osteoporosis, an apparatus measures bone mineral density (BMD). BMD is usually reported in standardized form. The standardization is based on a population of healthy young adults. The World Health Organization (WHO) criterion for osteoporosis is a BMD value of less than 2.5 standard deviations below the mean for young adults. BMD measurements in a population of people similar in age and sex roughly follow a normal
• If a group of athletes have a mean BMD of 1.1 and same standard deviation as young adults, what percent of this group have osteoporosis by the WHOcriterion?
• Women aged 60 to 69 are, of course, not young adults.  The mean BMD  in this age group is -1.2 (negative two) on the scale for young adults. Suppose that the standard deviation is the same as for young adults. What percent of this older population hasosteoporosis?
• • Customers arrive at an ATM inside a shop at a rate of 10 per
  • What is the probability that the next customer will arrive in 30 minutes?
  • What is the probability that there will be no customers next hour?

2.

• An operator for a telephone-answering service answers a large number of calls for two companies A and B. Company A is charged double the monthly fee of Company B under the assumption that Company A will receive approximately double the calls coming in for Company B. If this assumption is correct, find the probability that in the next 100 calls 70 or more will be for Company A. (Use normal approximation of the binomial)
• The persons seeking employment with the National Australia Bank will haveto take an online test given by the bank. From historical data it is found that the scores of the applicants are normally distributed with a mean of 57 and a standard deviation of
• If one applicant is selected at random, what is the probability that his or her score will be between 54 and63?
• In a random sample of 36 test scores, what is the probability that the sample mean will be between 58 and60?
• The mean of these 36 test scores has the probability of 0.2206 of exceeding a certain number. What is that number?

3.

• A Malamal Weekly poll on lottery tickets interviewed 320 women and 580 men randomly selected from shoppers in a news agent. The poll found that 13% of the women said they do not check their numbers against the result after the
  • The poll announced a margin of error of ±4% for 95% confidence in conclusions about women. What is the implication of reporting the margin of error instead of just stating that 13% of women do not check their numbers against theresult?
  • Will the margin of error for men be the same, higher or lower? Why?
  • A test for the level of potassium in the blood is not perfectly precise. Moreover, the actual level of potassium in a person's blood varies slightly from day to Suppose that repeated measurements for the same person  on different days vary normally with s=3 .
    • Julie's potassium level is measured once. The result is x = 4.1. Give a 99 percent confidence interval for her mean blood potassium
    • If four measurements were taken on different days and the mean result is x =05 , what is a 99% confidence interval for Julie's mean blood potassiumlevel?

4.

• A manager of public health services in an area downwind of a nuclear test site wants to test the hypothesis that the mean amount of radiation from an isotope in the bone marrow (measured in picocuries) for citizens who live downwind of the site does not exceed that of citizens who live upwind from the site. It is known that citizens living upwind have a mean level of the isotope of 2 picocuries. Measurements of the isotope radiation for a sample of n = 16 citizens who live downwind of the site was taken, with the result given in the accompanying list. Assume normality and use a significance level of 0.01 to perform the test of  hypothesis. 6 2 2 2 2 5 5 7 1 1 0 2 0 3 4 3
• In the past, the life of a certain brand of Goodyear tyre has been 40,000 kilometres with a standard deviation of 5,000 kilometres. Engineers redesigned the tyre and tested the mileage of a simple random sample of 64 new
  • On the average, how many kilometres must this sample of 64 tyres last for the tyre manufacturer to conclude that the new tyre yields a higher mileage than the old tyre? The manufacturer is willing to run a risk of no more than 5 percent of drawing such a conclusion in (Assume standard deviation isunchanged.)

Suppose that the sample mean for the new tyre is 41,000 kilometers, and you use the standard error established in part (i). What is the probability of reaching an incorrect conclusion? Will that be a Type I or Type II error? 5. A restaurateur believes that the day does not make a difference as to the number of patrons who visits his restaurant per day. To verify his assumption he records the number of patrons he gets on different days and the data is provided below: Test if the assumption of the restaurateur is correct at 0.10 level of significance. If his assumption is wrong, is Saturday significantly different from Sunday? 6. It is believed that the freight cost in bulk shipping is linearly related to the weight of the freight. The table below provides some data on weight and freight cost.

• Find a linear regression equation for freight cost with weight as the independent variable.
• What is the value of the Coefficient of determination (R-square)?
• Plot the residual values and comment if there is any pattern in the

7.

• The data on the value of an asset is given in the following table. Use exponential smoothing with a smoothing coefficient (W) of 0.25 to forecast the asset value in

• Prices of five items in years 2002 and 2008 are given in the table Calculate the CPI of 2008 with 2002 as the base year and for all five items using Paaschemethod.

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