# Linear Correlation Coefficient Worksheet

Linear Correlation Coefficient Worksheet
• Page 1
1.
Select the correct statement(s).
I. A point estimate is a specific numerical value estimate of a parameter.
II. The sample mean is a better estimator of the population mean than the sample median or sample mode.
III. Of all the statistics that can be used to estimate a parameter, the relatively efficient estimator has the smallest variance.
 a. I, II and III b. I and III only c. II only d. I only

#### Solution:

A point estimate is a specific numerical value estimate of a parameter.
[Definition.]

The means of samples vary less than other statistics. So, mean is considered as a better point estimate.

In order to represent the value of the parameter estimated, the estimator shall be as close as to the value that is, the variance shall be minimum.

So, all the statements are correct.

2.
Select the correct statement(s).
I. An interval estimate always contains the value of the parameter being estimated.
II. To be more confident that the interval contains the true population mean, the interval shall be more narrow.
 a. I only b. II only c. none d. I and II

#### Solution:

An interval estimate may or may not contain the value of the parameter being estimated.

To be more confident that the interval contains the true population mean, the interval shall be wider.

So, both the statements are wrong.

3.
If 95% confidence interval for the average age of the club members is 39 < μ < 41, then which of the following could be 99% confidence interval?
 a. 39.4 < μ < 40.6 b. 39.5 < μ < 40.5 c. 39 < μ < 41 d. 38 < μ < 42

#### Solution:

To be more confident that the interval contains the true population mean, the interval shall be wider.

38 < μ < 42 is the most suitable choice for 99% confidence interval for the average age of the club members.

4.
For a sample mean of 35.3, and a given standard deviation the 95% confidence interval for a population mean was calculated as 33.894 < μ < 36.316. Which is the correct representation after rounding the values?
 a. 33.894 < μ < 36.316 b. 33.89 < μ < 36.32 c. 34 < μ < 36 d. 33.9 < μ < 36.3

#### Solution:

Rounding is done to the same number of decimal places of the sample mean.

33.9 < μ < 36.3 is the correct representation of the interval.

5.
The maximum difference between the point estimate of a parameter and the actual value of the parameter is called the _____ .
 a. interval estimate b. range of the estimate c. maximum error of estimate d. standard deviation

#### Solution:

The maximum difference between the point estimate of a parameter and the actual value of the parameter is called the maximum error of estimate.

6.
When a 95% confidence interval is calculated instead of a 90% confidence interval with the same sample, the maximum error of estimate will be _____ .
 a. either smaller or larger depending on sample size b. the same c. smaller d. larger

#### Solution:

When the confidence level is increased, the possibility of error is more.

So, the maximum error of estimate in a 95% confidence interval will be larger than that in a 90% confidence interval.

7.
Determination of sample size depends on:
I. sample variance
II. population standard deviation
III. degree of confidence
IV. maximum error of estimate
 a. II and III only b. all of the above c. II, III and IV only d. I, III and IV only

#### Solution:

Sample size determination is closely related to statistical estimation.

It depends on three things: population standard deviation, degree of confidence and the maximum error of estimate.

The correct answer is II, III and IV only.

8.
Select the correct representation of a 95% confidence level case.

 a. figure - 1 b. figure - 4 c. figure - 3 d. figure - 2

#### Solution:

For 95% confidence level, = 1 - 0.95 = 0.05

Area in the right tail = 0.05 / 2 = 0.025

Area in the left tail = 0.025

Figure - 4 is the correct representation.

9.
What is meant by 95% confidence interval of the mean?
 a. 95% of the specific sample means will fall within ± 1.96 standard errors of the population mean. b. 95% of the specific sample means will fall within ± 2.58 standard errors of the population mean. c. There is 95% probability that the sample mean is equal to the actual population mean. d. standard deviation of the population mean = 5

#### Solution:

When the sample size is large, approximately 95% of the sample mean will fall within ± 1.96 standard errors of the population mean.
[Central limit theorem.]

Value of 1.96 corresponds to 95% confidence level taken from standard table of the t distribution.

10.
Which of the following statement(s) is/are true for correlation?
I. If the change in one variable affects a change in the other variable, the variables are said to be correlated.
II. Correlation coefficient is independent of change of origin and scale.
III. If $r$ = 1, then the correlation is perfect and positive and
if $r$ = - 1, then the correlation is perfect and negative.
IV. Two independent variables are correlated.
 a. II and III only b. I, II and III only c. IV only d. I only

#### Solution:

If the change in one variable affects a change in the other variable, then the variables are said to be correlated.

Correlation coefficient is independent of change of origin and scale.

Correlation is perfect and positive when r = + 1 and perfect and negative when r = - 1.

Two independent variables are uncorrelated.

So, only I, II and III statements are correct.