Title
by Name Here
Subject
Professor
University
City
Date
Business Mathematics
Student No.:
Question 1
a.
b.
c.
We can infer by visual inspection from the bar graphs that the disparity between the qualifications held by men and women for almost all levels is not that different from each other. While there are more females under the no qualification level, the unknown levels were seen to be dominated by males. Still, these differences are not considered to be economically significant. More importantly, the known levels from 1 through 5 were found to be almost equal.
Question 2
a.
b.
c.
The data from Fig. 3 alone shows a “seasonal” trend for the sales of bread wherein a given week is subject to various fluctuations and yet these fluctuations are seen to occur in a pattern that is consistent in all three weeks of analysis. For instance, the lowest sales usually occur on Tuesdays and then the trend would slowly creep up until reaching its peak on Saturdays. It was also consistent that the biggest decline happens from Saturday heading to Sunday.
The behavior of the 7-day moving average gives a much stable report on the daily sales of the bakery. From the moving average line, the average sales lie at around 40 to 50 loaves. The trendline also suggest a slight rise in sales throughout the period.
Question 4
a.
b.
The correlation coefficient was computed to be .
c.
The regression equation for predicting the time to pay given a price value is
d.
From the results obtained, the correlation coefficient represents the direction and the strength of the relationship between the expected time to pay given a certain value. For the gas company, the high value of suggests that higher values of amount due result in longer payment time while lower values require shorter period, and this relationship is extremely consistent.
The gradient or slope, which is equal to 0.0404 means that for every pound increase of amount to be paid, there is a 0.0404-day increase in time to wait for a complete payment. Another way of looking at this value is that an expected 1-day increase in waiting period is due to a 24.77-pound increase in the amount owed. The intercept of 11.129 represents a correcting offset for the entire regression itself. This value should be cautiously used and should not be misinterpreted that if there no money to be paid, then the gas has to wait 11.129 days. This is where the limitation of the equation should be considered given that the analysis was done with at least £100 as a data point.
e.
The coefficient of determination or is 0.792. This means that the regression equation mentioned above explains 79% of the variance of the response. This value can be considered to be high which therefore says that the regression model is accurate in describing the variance of the number of days to payment.
f.
If the amount to be paid is £125, the expected days to pay is 16.17 days while for a £1000 owe, the time is 51.49 days. An obvious reservation that can be taken for this prediction is the fact that no one from the sample data points owed higher than £480. For an amount that is extremely out of the usual range, predicting the number of days should be taken with caution.
Question 4
a.
Table 1. Frequency table for item weights (g) produced by machine. | |
Weight (g) | Frequency |
2 | |
0 | |
3 | |
5 | |
6 | |
10 | |
7 | |
10 | |
10 | |
11 | |
12 | |
4 |
b.
c.
Using Excel, the descriptive statistics including the 95% confidence interval of the mean was computed and are summarized in Table 2 below.
Table 2. Weight (g) descriptive statistics summary. | |
Mean | 27.2375 |
Standard Error | 0.295484878 |
Median | 27.4 |
Mode | 30 |
Standard Deviation | 2.642897097 |
Sample Variance | 6.984905063 |
Kurtosis | -0.381752838 |
Skewness | -0.458029005 |
Range | 11 |
Minimum | 20.4 |
Maximum | 31.4 |
Sum | 2179 |
Count | 80 |
Confidence Level(95.0%) | 0.588147938 |
The computed average value of weight output was at 27.24 g. Based on the generated histogram as well as the skewness, the distribution is negatively skewed which means more data tend to cluster at the higher end while very few is on the lower side. The negative kurtosis suggests that the distribution is relatively flat, which means no particular value is exceedingly more frequently appearing than the others. Also, the data has a wide range from 20.4 to 31.4 but the computed confidence interval for the mean was narrow at ±0.588. In other words, should the sampling be repeated, 95% of the time, the true mean will lie in those confidence intervals, which for this particular sample is at 26.65 to 27.82. This is a strong evidence to support the claim that the mean output of the machine is greater than 26 grams.
References
Cox, D. R. & Hinkley, D. V., 1974. Theoretical Statistics, s.l.: Chapman & Hall.
Frost, J., 2013. Regression Analysis: How Do I Interpret R-squared and Assess the Goodness-of-Fit?. [Online]
Available at: http://blog.minitab.com/blog/adventures-in-statistics/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit
[Accessed 9 December 2016].
Frost, J., 2013. Regression Analysis: How to Interpret the Constant (Y Intercept). [Online]
Available at: http://blog.minitab.com/blog/adventures-in-statistics/regression-analysis-how-to-interpret-the-constant-y-intercept
[Accessed 5 December 2016].
Groebner, D. F., Shannon, P. W., Fry, P. C. & Smith, K. D., 2005. Business Statistics: A Decision-Making Approach. 6th ed. s.l.:Peason Education, Inc..
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