HI6007 Shape Of Histogram

1. Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set using a class width of $50. (3 marks)

b. Construct a histogram showing the percent frequency distribution of the furnitureorder values in the sample. Comment on the shape of the distribution. (3 marks)

c. Given the shape of the distribution in part b, what measure of location would be most appropriate for this data set?

Answer:

Frequency, Relative Frequency and % Frequency.

Histogram 

èShape of histogram – Positive skewness, the frequency distribution for furniture order is Left skewed and depicts the prices to be focused from $150 to $250.

Mode is the best typical location that is best for this specific data set. This is primarily because the similar pres have occurred more than once and especially in class “$150- $200”. Hence, the number of frequency is more in this class range.

The two variables “Demand and unit price” are related and can be further emphasized through t significance which is 0. At 95% level of significance; p < 0.05. Alternatively, in this scenario, p value is less than 0.05, which is showing the independent and dependent variable to be related.

è Coefficient of determination = SSM / SST = 0.6171 = 61.71% variations.

Coefficient of determination examines whether the model is best fit or not. In this case, model is a good fit because 61.71% of the variations in Y (demand) are explained by X (price).

èr =   = 0.7855

Based on the above result, demand and price are positive correlated and being more than r>0.5, it is strongly correlated as well. Hence, change in price will affirm the change in demand whether it is positive or negative. 

H₀: There is no significant difference among the means of the three populations.

H₁: There is significant difference among the means of the three populations.

At 95% level of significance; p < 0.05 for F statistics. Alternatively, in this scenario, p value is less than 0.05, which is showing the independent and dependent variable to be related. In this case, p value < 0.05 gives statistically valid results. Hence, there is significant difference among the means of the three populations (α=0.05).

è Y = 0.8501 + 0.4977*X₁ + 0.4733* X₂

è Phones sold per day = 0.8501 + 0.4977*Price + 0.4733*Advertising spots

At 95% level of significance; p < 0.05 for F statistics. Alternatively, in this scenario, p value = 0.001 which is less than 0.05, which is showing the independent and dependent variable to be related. In this case, p value < 0.05 gives statistically valid results (α=0.05).

H₀: β1 and β2 is not significantly different from zero. .

H₁: β1 and β2 is significantly different from zero.

At α = 0.05, β₁ has p = 0.32246> 0.05, making it not significantly different from zero. Hence, accepting null hypothesis is case of β_1. 

Whereas, at α = 0.05, β₂ has p = 0.00 < 0.05, making it significantly different from zero. Hence, rejecting null hypothesis is case of β₂

The slope coefficient for X₂ (β₂) = 0.473. Hence, this illustrates that with one unit change in X₂, and then Y would be changed by 0.4733 units. Even though, the relation is directional such as increase in X₂ will lead to positive change in Y/

Y = 0.8501 + 0.4977*X₁ + 0.4733* X₂

è Y = 0.8501 + 0.4977*20 + 0.4733*10

è Y= 0.8501 + 9.954 + 4.733

è Y = 15.5371 ≈ 16 = Phones sold per day