HI6007 Group Assignment

Construct a frequency distribution, cumulative frequency distribution, relative frequency distribution, cumulative relative frequency distribution and percent frequency distribution for the data set using a class width of 10. (5 marks)

 

Construct a histogram showing the percent frequency distribution of the examination scores. Comment on the shape of the distribution.

Question 1

The frequency scores were only for the first class (52 to 62). This implies that a class width of 10, used in was too wide to accommodate the scores that were of a small margin range.

Question 2

1. Sample size

Df =n-1

Df+1 = n

(39+1)+1 =41

MS (mean square) = SS/df

MStreat = SStreat/df treat

= 354.689/1

= 354.689

MSres = SSres/dfres

= 7035.262/39

= 180.39

F value = MStreat/MSres

= 354.689/180.39

=1.97

Since the f value (1.97) is greater than the alpha value of 0.05, it implies that demand and unit price are not related

1. Coefficient of determination (r²)

R² = SSR/SSTO,

Where SSR = regression sum of squares

SSTO = total sum of squares

R²  = 354.689/7035.262+354.689

= 354.689/7389.951

= 0.048

The coefficient of determination is less than 1, meaning this is a lower coefficient and poor indicator of goodness of fit. The predictor X doesn’t account for all the variations in Y. in other words, the unit price doesn’t affect the supply at times. For every change in the unit price, the supply unit doesn’t change automatically.

1. Coefficient of correlation – r

R =√r²

= √0.048

= 0.21

This is a positive correlation, however, it is a weak positive correlation since r is not close to 1. This indicates that there is a relation between supply and unit price, such that for every change in unit price there is a corresponding change in the supply.

54. Y = 54.076 + 0.029X

= 54.076 + 0.029 (50,000)

= 1,504.076 units.

Question 3

1. b) P value of 0.005 is less than 0.05, thus statistically significant. This implies that the introduction of the four different programs will increase productivity. Therefore, the company should go ahead and implement the programs.

Question 4

3. Y=3.58+41.32 (price)+0.01(advertisement)
4. The model is overall significant because the p value (0.053) is less than alpha value of 0.10
5. P value for price is 0.04, thus it is individually statistically significant in relation to sales because it is less than alpha 0.10. On the other hand, p value for advertisement is 0.97, thus, it is individually statistically insignificant in relation to sales.
6. Y=3.58+41.32 (price)
7. The slope coefficient of the above model is price. This implies that every change in price is a multiple of 41.32