SOCI 3311 Blog

Please explain False Practice Quiz question: If the correlation between X and Y equals .8, then 20% of the variance in Y is NOT explained by X.

True-False Practice Quiz 11 question: The correlation coefficient, r, detects any relationship between two variables. Answer if False. Please explain. "Correlation coefficient describes linear relationship between 2 variables. r indicates direction and strength of linear relationship between X,Y" (eText).

Also, If r<0, then as X increases, Y tends to increase. False. Please explain. "sign of r indicates +/- direction of relationship between X,Y. Numberical value r indicates strength of relationship between X,Y" (eText).

Problems 3, 4, and 5 of this assignment all require the 't test for independent samples.'

Problem 3 provides you with RAW DATA.

Problems 4 and 5 provide you with data that has been summarized (i.e. mean, standard deviation, sample size).

Hence, to work problem 3, you need the calculator labeled 't Test Ind. - Raw Data.'

To work problems 4 and 5, you need the calculator labeled 't Test Ind. - Sum. Statistics.'

For all three problems, you should provide:

(1) The null and research hypotheses
(2) Level of significance
(3) t critical (This is a t test not a z. To find t critical click the link labeled 'statistical Tables' and open the table labeled 'Distribution of t.')
(4) t obtained (This is the calculated value of t which you obtain when you use the appropriate online calculator.)
(5) Decision (i.e. reject Ho or fail to reject Ho)

Here is the solution to Problem 5:

H(0): μ(1) = μ(2)
H(1): μ(1) ≠ μ(2)
α = .05
t critical (df= 118) = ±1.98
t obtained = 4.44
Since the absolute value of t obtained is greater than the absolute value of t critical, reject H(0)
There is a significant difference in the average number of errors made for these two groups.

Notice the value 118 is NOT in the table of t values. For simplicity's sake, just use the value CLOSEST to 118 (regardless of whether it is under or over in value). Since 120 is the closest value in the table, I used 1.98.

I got and F critical of 4.38 and F obtained of 30.01. Is that correct? And if it is, that means we reject H(0) and there is a diff in the average, right? Do you want us to stop there or do we continue to determine which season is unequivalant?

Problem 3:

3-1. To answer this question, open the calculator labeled CORRELATION ANALYSIS and enter the data to create a graph. You should be able to see if the relationship is generally positive (as X increases, Y increases) or negative (as X increases, Y decreases).

3-2. From this same graph you should also be able to determine if the data general form a straight line (linear) or something else (non-linear).

3-3. From CORRELATION ANALYSIS calculator, you will also see a value labeled 'r = ##.' This is the correlation coefficient. If the correlation coefficient is close to zero, there is no relationship. The closer the value of r is to 0, the WEAKER the relationship. The closer the value to ±1.00, the stronger the relationship.

3-4. To answer this question you will need to open the calculator labeled CORRELATION AND REGRESSION. Again, enter the data. When you click calculate, you are looking for Y' = a + bX (with values in place of a and b). Using this regression equation, substitute 700 (not 700,000) for X and calculated Y'. This is the answer.

3-5. To answer this question, square the correlation coefficient (r).


Problem 4:

4-1. The correlation coefficient is a number between -1.00 and +1.00. A value of 1.09 is out of range.

4-2. The correlation coefficient is 'unitless.' That is, no unit label is attached to a correlation coefficient.

5. This problem requires the use of the Chi Square Calculator. Open the chi Square calculator and enter the number of rows (3) and the number of columns (3). Now enter the table into the calculator and click calculate.

You need to complete the hypothesis testing steps for this problem.

Here is the solution:

H(0): Crime rate and temperature are independent of each other.

H(1): Crime rate and temperature not independent of each other.

α = .05

Chi Square obtained = 29.26

Chi Square critical = 9.49 (use the table of chi square values to find this where df = (rows - 1) X (columns - 1))

Because the calculated value of chi square is GREATER than the critical value of chi square, reject H(0). In other words, crime and temperature are not independent of each other.

When we use the calculator to compute the confidence intervals is the answer the calculator gives the final answer or do we need to break it down in to positive and negatives parts?

How are we supposed to determine which hypotheses to reject??

These four problems require use of the ONE SAMPLE Z calculator. Once you have computed z, use the following format to report your answer:

State the null and research hypotheses
State the level of significance (given in problem)
State the critical value of z (linked to the level of significance)
State the obtained (or calculated) value of z
State your decision

For Problem 4, your answer should appear as follows:

H(0): μ = 100
H(1): μ ≠ 100
α = .01
z critical = ±2.58
z obtained = 3.33
Decision: Reject H(0) and Accept H(1)

Use the same format for problems 5, 6, & 7.

For problem 5, you will need to first use the DESCRIPTIVE CALCULATOR to find the sample mean and sample standard deviation before you can use the ONE SAMPLE Z CALCULATOR.

All of this is explained in Unit 7.

Can anybody tell me how to get started with these three problems? I just attempted to do them but once I clicked on the calculator, it asked for information that I couldn't find. Blog back or just send me a message.


~Caryn C.~

Problems 7 and 8 of this assignment require the 'Analysis of Variance' test.

Because both problems have 4 groups or samples, you will need to use the calculator labeled 'ANOVA - 4 Samples.'

In both cases, you should provide the following:

(1) Null and Research Hypotheses
(2) Level of Significance
(3) F Critical (This is not a z or t test. It is an F test - hence, F critical.)
(4) F Obtained (This is the calculated value of F obtained when you use the ANOVA calculator.)
(5) Decision

Here is the solution to Problem 8:

H(0): μ(A) = μ(B) = μ(C) = μ(D)
H(1) not all means are equal
α = .05
F critical (3,12) = 3.49 (Because F is the ratio of 2 variance estimates, we have degrees of freedom for each estimate -- i.e. numerator and denominator degrees of freedom).
F obtained = .30
Decision: Fail to reject H(0)
The drying time is the same for all four brands of clothes dryers.

To find the critical value of F, please click on 'statistical tables' and open the table labeled 'Distribution of F.'

For more detail on Analysis of Variance, please see Unit 10.

To work this problem, it is important to understand the relationship among the various components of an F table.

	DF	Sum of Squares	Mean Square	F
Total	16	220	13.75
Between	7	140	20	2.25
Within	9	80	8.89

I've displayed in normal type those values are you given.

I've displayed in BOLD type those things I've computed.


Remember:

Total Degrees of Freedom = Between Degrees of Freedom + Within Degrees of Freedom

Total Sum of Squares = Between Sum of Squares + Within Sum of Squares

Total Mean Square = Total Sum of Squares / Total Degrees of Freedom

Between Mean Square = Between Sum of Squares / Between Degrees of Freedom

Within Mean Square = Within Sum of Squares / Within Degrees of Freedom

F = Between Mean Square / Within Mean Square

On 1-2 I thought it was false because the mean is just an average and does not show any variation without other data to relate it to but (some indication) seemed slightly vague. On 1-9 i originally thought it was false because I know the mean is zero and the standard deviation is one, but the variance is the square of sd, and one squared is one so my second thought would be true.

Is this question giving us the variance or do I use the figures given to calculate the variance, then standard deviation? so does s2=25 or does s2=250?

On number 10, you are given the standard deviation of the sample. Because we do not know the population standard deviation, we will substitute the sample standard deviation.

This means we need the t value (instead of z value) associated with the 95% confidence Interval.

To find this value, open the link labeled STATISTICAL TABLES and click on the table labeled 'distribution of t.'

Select level of significance = .05 (.05 +.95 = 1.00) for 2-tailed test and N=49. Since 49 is NOT in the table, simply select the closest value (over or under - it will be close enough). t (df=40 is the closest)= 2.021.

Now use the CONFIDENCE INTERVALS calculator.

Enter:

Population mean = 5
standard deviation = .49
t = 2.021
Sample Size = 49

You should get 5.00 ±.14

Go to CALCULATORS. Select the calculator labeled CONFIDENCE INTERVALS.

For 8-1:

Enter the following:

Population Mean = 110
Population Standard Deviation = 12
z = 1.96 (because we are using a 95% confidence interval -- if we were using a 99% confidence interval, z = 2.58)
Sample Size = 100

ANSWER: 110 ±2.35

You can leave the answer like this or you can subtract 2.35 from 110 and add 2.35 to 110 and display answer as follows:

107.65 - 112.35

Either is acceptable (correct)

Work Problem 9 the same way but use z=2.58

3-1:

H(0): μ = 5 mm
H(1): μ ≠ 5 mm

I'm going to let you try Part 2. If you need help, just let me know.

4. Your answer should appear as follows:

H(0): μ = 100
H(1): μ ≠ 100
α = .01
z critical = ±2.58
z obtained = 3.33
Decision: Reject H(0) and Accept H(1)

All of this is explained in Unit 7.

if i received the standard deviation from the calculator, can i just square that number to get the variance? logically i would think so since the standard deviation is the square root but double checking.