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Introductory statistics questions.

Introductory statistics questions.

Find Introductory statistics university examination questions in acaproso.com

# Question
1

Explain briefly the four sampling methods


Short answers
2

Time magazine collected information on all 464 people who died from gunfire in the Philippines during one weak. Here are the ages of 50 men randomly selected from that population.

19 18 30 40 41 33 73 25 23 25
21 33 65 17 20 76 47 69 20 31
18 24 35 27 21 36 65 70 22 25
65 16 24 29 42 38 26 46 27 65
21 27 23 25 71 37 75 25 27 23
  1. Construct frequency table
  2. Compute mean, median, mode and standard deviation

Mathematical Calculation
3

The mean and standard deviation of  a set of 100 observations were found to be 35 and 4 respectively. If the observations 39,32,34 were omitted from the 100 observations, find the mean and standard deviation of the remaining 97 observations.


Mathematical Calculation
4

Calculate the mean, mode, median and standard deviation, range and interquartile range of the following items; 65, 55, 89, 56,35,14,56,55,87,45,92.


Mathematical Calculation
5

The age and blood pressure of 10 women are:

AGE 56 42 36 47 49 42 60 72 63 55
BLOOD PRESSURE 147 12 11 128 145 140 155 164 149 150
  1.  Compute correlation coefficient between blood pressure and age.
  2. Compute coefficient of determination
  3. Estimate linear regression of  blood pressure on age and state whether it is a good or poor fit.
  4. Estimate the blood pressure of a woman whose age is 45 years.

Mathematical Calculation
6

Briefly explain the following terms.

  1. Sample
  2. Scatter diagram
  3. Mutually exclusive events
  4. Interval estimation
  5. Type 1 error

Short answers
7

Last year, five randomly selected students took a math aptitude test before they began their statistics course. The table below shows scores on the aptitude test and statistics grades.

Student 1 2 3 4 5
Scores on Math aptitude test(X) 95 85 80 70 60
Statistics test(Y) 85 95 70 65 70

Use the table to answer the following questions

  1. Regress Y on X and interpret the constant coefficient and slope parameter
  2. If a student made an 80 on the aptitude test, what grade would we expect him/her to make in statistics?
  3. How well does the regress on the equation fit the data?

Mathematical Calculation
8
  1. X is a random variable such that Xsim Bin(n,p) . Given that E(X)=2.4 and p=0.3, find the value of n.
  2. Let the random variable X represent the number of boys in a family.
  1. Construct the probability distribution for a random variable X in a family of three children (assuming that the chance for a boy to be born is  frac{1}{2} )
  2. Show that X is a random variable.
  3. Find the expected value and standard deviation of X.
  1. The mean number of bacteria per milliliter of liquid is known to be 4. Assuming that the number of bacteria follows a Poisson distribution, find the probability that , in 1 ml of liquid , there will be four bacteria.

Mathematical Calculation
9

The same test was given to a group 100 scouts and to a group of 144 guides. The mean score for the scouts was 27.53 and the mean score for the guides was 26.81. Assuming a population variance of 12.11 for both scouts scores and guides scores;

  1. Construct a 95% confidence interval for the difference between population means of scouts scores and guides scores and interpret the results.
  2. Test whether the scout`s performance in the test is the same to that of guides at 5% level of significance, assuming that the scores are normally distributed. Use the general procedures for testing hypothesis.

Mathematical Calculation
10

Frequency distribution of age at loss of last tooth is given below:

Age 11-15 16-19 20-24 25-29 30-34 35-39 50-54 55-74
Frequency 1 7 21 35 40 58 28 10

Find

  1. Mean
  2. Median
  3. Mode

Mathematical Calculation