HA1011 Applied Quantitative Methods

Question 1

1. Frequency distribution table

Table 1

1. Histogram

Figure 1

1. Measures of central tendency

Table 2

Question 2

1. The above is a sample and not a population. A population refers to the entire largest set of items that a study is interested in while a sample is a subset of a population.
2. Standard deviation
3. Interquartile range

Therefore the lower quartile is in 1.75^th position after arranging the data in order from the smallest to the largest.

5884, 6014, 6214, 6916, 7209, 7223, 8158

1.75^th position is between 5884 and 6014, thus 1^st quartile = (5884 +6014)/2

Therefore the upper quartile is in 5.25^th position after arranging the data in order from the smallest to the largest.

5884, 6014, 6214, 6916, 7209, 7223, 8158

5.25^th position is between 7209 and 7223, thus 3^rd quartile = (7209 +7223)/2

1. Correlation coefficient

From excel output we have,

Table 3

It can be observed that the correlation coefficient between number of chocolate bars sold per week and weekly attendance is 0.98. This indicates that the two variables are highly correlated. This indicates that more chocolate bars are sold when more Holmes students attend classes and the converse is also true. It is therefore advisable for the manager of the supermarket to stock less chocolate when Holmes is closed during the holidays.

Question 3

1. Regression equation

Where b is the slope and c is the y-intercept

Table

It is the weekly attendance that affects the number of chocolate bars sold in a week. So weekly attendance is the independent variable (x) while number of chocolate bars sold in a week is the dependent variable (y)

When Holmes is closed it means x = 0

So to calculate the number of chocolate bars sold, we have,

When students increase by 10 we have;

1. Coefficient of determination

Coefficient of determination of 0.95 indicates that 95% of the variation in the dependent variable (number of chocolate bars per week) is caused by the independent variable (number of students attending Holmes in a week).

Question 4

1. Holmes or receiving grass root training

P (H or GR) = P (H) + P (GR)

1. External and scientific

P (E and SC) = P (E) X P (SC)

1. Scientific training in Holmes
2. Training is independent of from recruitment. This is because the sum of  the probability of all the possible outcome is equal to

Question 5

1. P (A and X)

P (A and X) = P (A) X P(X)

1. P (X= first preference)

Question 6

1. P (2 or less people)
2. Poisson distribution

Question 7

1. P (x>2,000,000)

Mean = 1,100,000

Standard deviation = 385,000

From the normal tables Z-value of 2.34 corresponds to a probability of 99.01%

Therefore P (x>2,000,000) = (100 - 99.01) = 0.99%

P (x>2,000,000) = 0.99%

1. P (1,000,00 < x < 1,100,000)

P (Z=0) = 50%

P (Z= - 0.26) = 60.26%

Therefore

Question 8