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HI6007 Statistics For Cumulative Frequencies And Frequency Percentages
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HI6007 Statistics For Cumulative Frequencies And Frequency Percentages
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Course Code: HI6007
University: Holmes Institute
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Country: Australia
Questions:
1. 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.
2. Construct a histogram showing the percent frequency distribution of the examination scores. Comment on the shape of the distribution.
Answer:
Construction of a frequency distribution table with cumulative frequencies and the frequency percentages
answer
group
frequency
Relative frequency
cumulative frequency
Relative cum
% frequency
50-59
3
0.15
3
0.15
15
60-69
2
0.1
5
0.25
10
70-79
5
0.25
10
0.5
25
80-89
4
0.2
14
0.7
20
90-99
6
0.3
20
1
30
construction of histogram
The histogram trends upwards indicating that individual students’ performance was good
sample size for the problem
39+1=40
Determine whether or not demand and unit price are related. Use α = 0.05.
Answer
We compute the t-value
The associated p-value is 0.399008; this value is greater than 0.05, we therefore fail to reject the null hypothesis and conclude that there is no relationship between the sales and individual prices of the goods produced.
Compute the coefficient of determination and fully interpret its meaning. Be very specific.
Y=54.076+0.029x
The coefficient of determination is 0.047996; this implies that 4.7996% of the variation in the dependent variable is explained by the independent variable in the model.
Compute the coefficient of correlation and explain the relationship between supply and unit price.
The coefficient of correlation is 0.21921; this shows that a weak positive relationship exists between demand and price. That is, increasing demand would result to an increase in the price.
Predict the supply (in units) when the unit price is $50,000
Y=54.076+0.029(50000)
=$1504.076
Construction of ANOVA table for the increase in productivity through programs A to D
hypotheses
H1:the programs A to program D have got no significant increase in the productivity of cooperation’s line workers
H2: the programs A to program D have got significant increase in the productivity of cooperation’s line workers
ANOVA table
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Program A
5
725
145
525
Program B
5
675
135
425
Program C
5
950
190
312.5
Program D
5
750
150
637.5
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
8750
3
2916.667
6.140351
0.00557
3.23887
Within Groups
7600
16
475
Total
16350
19
(α=0.05)
Advise
Since the computed F (6.140350877) is greater than the critical F (3.238871517) and the p value 0.005569864 is less than 0.05, we reject the null hypothesis and conclude that there is a significant increase in production from the programs applied. We therefore advise the company to continue with the programs.
What is the estimated regression equation? Show the regression output
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
3.5976
4.0522
0.8878
0.4248
-7.6532
14.8484
Price (x1)
41.3200
13.3374
3.0981
0.0363
4.2896
78.3505
Advertising (x2)
0.0132
0.32759
0.0404
0.9697
-0.8963
0.9228
Determine whether the model is significant overall. Use α = 0.10.
ANOVA
df
SS
MS
F
Significance F
Regression
2
45.35284
22.67642
6.716801
0.052644
Residual
4
13.5043
3.376075
Total
6
58.85714
As can be seen I the above table, the p-value for the F-statistics is 0.0526 (a value less than α = 0.10), this leads to rejection of the null hypothesis and thus we conclude that the overall model is significant at α = 0.10.
Determine if competitor’s price and advertising is individually significantly related to sales. Use α = 0.10.
Competitors price vs sales
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
3.5818
3.6082
0.992676
0.366447
-5.69342
12.857
Price
41.6031
10.1552
4.096719
0.009385
15.49825
67.70786
Advertisement vs sales
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
14.71053
3.108829
4.731854
0.005188
6.719026
22.70203
Advertisement
0.546053
0.459802
1.187582
0.288334
-0.63591
1.728011
Independently, the competitor’s price has got a significant relationship on the sales of goods as the p value, 0.00938 while the advertisement has got no significant relationship with the sales of the product as the value 0.28833 is greater than the hypothetical 0.10
Based on your answer to part (c), drop any insignificant independent variable(s) and re-estimate the model. What is the new estimated regression equation?
Answer
The insignificant variable is the advertisement and it is dropped thus the new regression equation is;
Interpret the slope coefficient(s) of the model from part (d).
Answer
The slope coefficient for the competitor’s price is 41.6031; this implies that a unit increase in the competitor’s price would result to an increase in the sales made by 41.6031. Similarly, a unit decrease in the competitor’s price would result to a decrease in the sales made by 41.6031.
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