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.

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 |

[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.

Correct answer : (1)

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.

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 |

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

So, both the statements are wrong.

Correct answer : (3)

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 |

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

Correct answer : (4)

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 |

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

Correct answer : (4)

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 |

Correct answer : (3)

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 |

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

Correct answer : (4)

7.

Determination of sample size depends on:

I. sample variance

II. population standard deviation

III. degree of confidence

IV. maximum error of estimate

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 |

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.

Correct answer : (3)

8.

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

a. | figure - 1 | ||

b. | figure - 4 | ||

c. | figure - 3 | ||

d. | figure - 2 |

Area in the right tail =

Area in the left tail = 0.025

Figure - 4 is the correct representation.

Correct answer : (2)

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 |

[Central limit theorem.]

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

Correct answer : (1)

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.

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

if

IV. Two independent variables are correlated.

a. | II and III only | ||

b. | I, II and III only | ||

c. | IV only | ||

d. | I only |

Correlation coefficient is independent of change of origin and scale.

Correlation is perfect and positive when

Two independent variables are uncorrelated.

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

Correct answer : (2)