Quantitative Analysis
Question 1
A 95% confidence interval means that the estimate of the income of the shop assistants is up to the mentioned percentage. This means that the shop assistant’s income ranges between $12,000 and $15,000 and the estimate’s reliability is 95%. A 99% confidence interval is better than 95%. This is because the level of reliability of estimate at 99% is better than that at 95%.
Question 2
The z-score for 40
(50-40)/6 = 1.66
Probability P is less than 40=1-1.66=-0.66
Question 3
48% is a good estimate of the proportion of all students who own a laptop. This is because it factors in the total number of students and the specific number that has laptops.
Question 4
With a standard deviation of 12.5, the population is big since it means that the data is quite spread.
Question 5
With a significance level of 1%, a test would be showing that the results are true to the 1% and the probability is not by chance to that extend.
At 10% level, the reliability of the test is higher than that of 5% level.
Question 6
Reducing the price to $75, the cameras sold will be 50.
The cost of acquiring them =50*$50=$2,500
The sales amount will be $75*50=$3,750
The profit will be $1,250
Question 7
(a) Hypothesis testing refers to the process of making a decision whether results obtained from experiments form a base for doubt regarding the normally accepted situation. In research, hypothesis testing is very important. Hypothesis is very important in statistics since it helps in coming up with a conclusion regarding the occurrence of a given thing. To summarize it, the purpose of hypothesis testing is to decide whether the data used in a given situation is significant statistically.
(b) Sampling is the other thing that is important in statistical analysis. The purpose of sampling is to make the research process easy. Sampling is usually very useful in simplifying a statistical analysis.
Question 8
- Decision tree for the shop problem is as follows
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(b). The shoe store should be located in the new centre.
(c)The decision tree would take one path with perfect forecasting
Question 9
Unemployment is responsible for the slowing down the sales for each state.
This model is better since in statistics, adding more variables makes the test more reliable.
The other variables that could help in explaining sales include population increase and distribution. The increase in population determines the increase in demand thus affecting sales. The distribution of people in the market determines the level of sales in each region.
Question 10
- The components of time series include Secular trend, Seasonal variation, cyclical variation and Irregular variation.
Secular trend may be found in data related to production of goods for a given period.
Seasonal trend may be present in data related to amount of rainfall for given days of a season.
Cyclical variation may be observed in data related to performance of a student for two years. It is worth noting that for cyclical trend, the period has to be at least two years (Upton & Cook 2001).
Irregular variation may be seen from the data of specific shares in the stock market.
b (i)
In 4th quarter, the electricity demand becomes very high for each of the five years. Secondly, the overall demand for household electricity has been going up each year.
b (ii)
The following shows that the 4-point centred moving average for Quarter 3 in 2007 is 5.025.
| Period(Quarter) | Value | Moving Average | Cantered |
| 1 | 5 | ||
| 1.5 | |||
| 2 | 4.7 | ||
| 2.5 | 5 | ||
| 3 | 4.8 | ||
| 3.5 | 5.025 | ||
| 4 | 5.5 |
References
Upton, G & Cook, I 2001, Introducing Statistics. Oxford University Press.
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