An index number measures the relative change in price, quantity, value, or some other characteristics of interest compared to a base period. It is a statistical value that measures the change in a variable with respect to the reference value of a variable for a specific period specific period such as a starting year, a specific factory or a specific location. The correct answer is C.

The null hypothesis can be µ1 – µ2 = 0

Systematic sampling method is applied easily by taking every kth element after a random starting point. The correct answer is D.

Depending on the number of variables included in the comparison, index numbers can be different. If an index number is used to measure the relative change in just one variable, this indicates a simple index. In the simple index calculation, the ratio of the two variables is converted to a percentage. In other words, index numbers are the percentage of a comparison with a reference value written without the percent symbol. It is important to determine what to write in the reference value field since the simple index calculations can be examined as a fixed based method and chain-based method. In applications, two types of indexes dominate, which are price and quantity indexes. The correct answer is B.

Since vehicles are substitute to each other, they are different decison alternatives.

In order to show the degree of the relationship between two continuous variables, The Pearson’s correlation coefficient or Pearson’s product moment correlation coefficient is widely used. There are two symbols used for Pearson’s correlation coefficient, population correlation is represented by ? (rho) and sample correlation is represented by r. Pearson’s correlation coefficient gets values between -1 and +1. If the result is exactly -1 or +1 then there is a perfect relationship between the variables. The sign of the Pearson’s correlation coefficient indicates the direction of the relationship. The positive sign indicates that the change in the variables is in the same direction.The Pearson’s correlation coefficient is a very useful tool to show the degree of the linear relationship between two variables. The Pearson’s correlation coefficient is not a perfect tool, and we should be careful while using it. First of all, Pearson’s correlation coefficient does not show the causal relationship. A relationship shown by Pearson’s correlation coefficient does not necessarily mean that one variable’s existence is the cause of the second variable’s existence. There may always many known or un-known effects on the existence of a variable. Pearson’s correlation coefficient is easily affected by the outliers. In order to control this problem, careful examination inspection of the relationship with a scatterplot will be very helpful. If a data pair is identified as an outlier or as unusual observations, the researcher may investigate the reasons of the existence of these values in such a problem and may or may not include these data points in his/her investigation. The study of outliers a very detailed subject and unfortunately will not be explained in this chapter. At the moment it is enough for you to know that if there are outliers, then the Pearson’s correlation coefficient value may not be correct, and the results should be studied in caution. The correct answer is therefore D. 

The statement in the question is the online stores mean price µ is less than the chain store, so the hypotheses are:

Null Hypothesis : H0 : µ = 180

Alternative Hypothesis :  H1 : µ < = 180

Since the components of the total variation is already given then the coefficient of determination for this problem is as follows:

r2 = explained variation / total variation = SSR / SST

SST = SSR+SSE = 450+ 50

SSR / SST = 450 /  (450+50) = 450 / 500 = 0.90 

Therefore, we can say that the 90% of the variability in the dependent variable can be accounted to the
independent variable.

(100 /120)*100 = 83.33

x = (4 / 3) . 100. pg. 140. Correct answer is B.

x = ((14. 5) / (25 . 4)) . 100 = (70 / 100) . 100 = 70 . pg. 145. Correct answer is D.

In a simple linear regression model, ? and ß refer to  the population parameters to be estimated by sample data.? parameter is the intercept of the regression line and ß is the slope of the regression line. ? parameter is usually called as the constant of the model. The correct answer is A. 

Index number = (200 / 50) * 100=400

The producer price index (PPI) is a family of indexes that measures the average change over time in selling prices received by domestic producers of goods and services. It is an output index and designed for domestic goods’ price changes; imports are not included. This index is based on the first commercial transaction of each product in non-retail markets. The correct answer is B.

x = (51 / 170) . 100 = 30

x = max = -0.2 . If the payoff table is based on costs, first for each decision alternative, the maximum payoff value of each decision alternative is listed then among these payoff values the decision alternative producing the minimum is chosen as the best decision alternative. pg. 190. Correct answer is A.