In order to investigate whether women are more likely than m

In order to investigate whether women are more likely than men to prefer Democratic candidates, a political scientist selects a large sample of registered voters, both men and women. She asks every voter whether they voted for the Republican or the Democratic candidate in the last election. This is

a).observational study

b)a random experiment.

c)A block design experiment.

d)None of the above.

19.       When the correlation coefficient is positive, it means:

a.There is a weak relationship.

b.When X goes up, Y does too.

c.X will not be a good predictor of Y.

d.When X goes down, Y tends to go up.

e.None of the above.

20.       A large sample of X-Y data values are analyzed and reveal a correlation coefficient of 1.12. Which statement is correct?

a.A fairly strong positive linear relationship exists between X and Y.

b.A fairly strong negative linear relationship exists between X and Y.

c. There is a computational error; correlation coefficient can not be greater

than 1.

d.There is no linear relationship between X and Y.

e.None of the above.

Solution

First Question ( 18 ) :

The answer is a) Observational study.
Reasoning:
In the given scenario the political scientist wants to draw an inference whether the women are more likely than men to vote for Democratic Candidates. For this purpose she has chosen a sample of previous year voters and on the basis of their reply the result will be inferred for the population. Thereby, the given scenario is an example of observational study where the inference from a sample is drawn to a population.

It\'s not a random experiment as the process of asking a voter can\'t be infinitely repeated as there are finite number of voters.

It\'s not a block design experiment as there is no variable of interest whose randomness is being blocked.

Second Question ( 19 ) :
The answer is b) When X goes up ,Y does too.
Reasoning:
The correlation coefficient is a measure of relative movement ( dependence ) of two or more variables. When the value of correlation coefficient is positive . It means that the involved random variables are positively correlated i.e the increase in value of one random variable will lead to increase in value of another random variable and vice versa.

Third Question ( 20 ) :
The answer is c) There is a computational error; correlation coefficient can not be greater than 1.
Reasoning:
1. The range of values which correlation coefficient can take is statistically defined to be -1 to 1.
2. When it\'s said that the correlation coefficient is 1 that means the random variables are perfectly correlated i.e at all time points of observation ( 100 % of the time ) the relation between the two variables is positive. It can also be interpreted this way that the random variables can\'t be observed more than 100% of the time to have a positive relation. Thereby, the maximum assigned value to correlation coefficient is 1.