1. 0.05 from the tables is 0.0199 And for the STA probability is 0.55
42 out of 70 give us a probability of 0.5833
0.55 > 0.5833, therefore there will be a high possibility that there will be an additional bus route
3. null hypothesis and alternative hypothesis: The first statement is correct
The null hypothesis is denoted as Ho; the null hypothesis is tested using a significant level using tables whereby when the table gives us the critical value and we have the calculated value, when the calculated value is greater than the critical value then we reject the null hypothesis.
If the calculated value is less than the critical value then we accept the null hypothesis, when we reject the null hypothesis in statistics then this means that we accept the alternative hypothesis. Statistical testing using the null and alternative hypothesis helps us show the significance or insignificance of estimated values in statistics.
4. below is the Z values
Correlation is a measure in statistics that shows the level or nature of the relationships that exists between variables, the correlation coefficient can be used to show whether the relationship that exist between two variables is linear or inverse. High correlation shows a strong relationship between the two variables being considered.
In an organization the correlation measure can be used to show the relationship that exists between the price variations of a product and the total sales, this measure therefore can be helpful in decision making regarding the price and other decisions made in an organization.
A regression is a model that is estimated to depict the depedent and indep[edent variable, it aids in finding out the relationship that exists between two or more variables, example a regression model concerning demand and price, in this model we can determine the demand if we change the price and this is done by estimating a regression model that shows the relationship between the price and the demand. If a regression model is statistically significant then it can be used in forecasting.
Risk analysis is similar to sensitivity analysis and it involves statistical testing of various options regarding investment that takes into consideration the risks that are involved in each option of investment given.
We regression models estimated regarding various variables in the firm in order to forecast on future outcomes of a business, forecasts are important in budget making and also achieving set objectives, the forecasted values therefore use the estimated models regarding sales and profits, the forecasts helps to make decisions regarding the business and if the regression represents the actual outcome then the business can achieve higher profits and sales when it uses these forecasts.
Sensitivity analysis involves the evaluation of the decisions to be made and the events that would occur which are out of control of the decision maker when such decisions are made. It helps firms to make decisions that take into consideration the events that are not controlled by the decision maker or the firm it but the events will be as a result of external factors that are uncontrollable. A business need to undertake sensitive analysis when undertaking decision making in order to make right decisions whereby the firm must take into consideration other decisions that will be made by competitors who use similar strategies.
The decision tree is a diagram that is useful in statistics due to the fact that it aids in decision making, given various decisions to be made and also the outcomes of those decisions made and their probability of occurrence then the firm is faced with some options to choose from, then decision tree is drawn and the total probability and outcomes are calculated and the firm will therefore make appropriate decisions. In firms this tree may be drawn to depict the best decision to make today regarding various investment options, the investment options may have future profits and also the probability of getting these profits.
This is a theory that depicts the behavior that exist between two firms that produce the same product in the market, given that there are only two firms in the market then if one firm reduces the price of its products then the other firm must follow the firm by also reducing its price for its products. If the firm decides to increase its price then the other firm will not increase its price. This is what is referred to as the game theory, it depicts that two firms in a market will make their decision by taking into consideration the actions of the other firm in the market.
The game theory is very important in decision made in firms whereby in a competitive market the firm will not increase its prices without taking into consideration the actions of its competitors. This theory therefore is useful in decision making.
6. The scenario on the Burns Auto Corporation defines the importance of statistics for business
in terms of forecasting and also risk analysis, the company adopts a strategy where they hire a financial consultant who develops a model that aids in forecasting sales levels of the firm. This is helpful as the variation in sales levels per month is considered. The model takes into consideration the sales level that depends on interest rates, income level, competitors and seasonal changes in sales.
Lind and Mason (2003) Statistical Techniques in Business and Economics,
McGraw Hill, New York
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