I have just a couple questions I have trouble understanding... can someone please help me?
The data below indicate the rankings of a set of employees according to class theory and on-the-job practice evaluations:
Theory 1 7 2 10 4 8 5 3 6 9
Practice 2 8 1 7 3 9 6 5 4 10
What is the Spearman correlation of coefficient for the data?
In an experiment, a sample size of 10 is drawn, and a hypothesis test is set up to determine: H0 : p = 0.50; H1:p < or = 0.50; for a significance level of .10, the decision rule is as follows:
A. Reject H0 if the number of successes is 2 or less.
B. Reject H0 if the number of successes is 8 or more.
C. Reject H0 if the number of successes is three or less.
D. Reject H0 if the number of successes is less than 2 or more than 8.
To find the Spearman correlation coefficient for the given data, you will need to follow these steps:
Step 1: Assign ranks to the Theory and Practice data separately. Assign ranks based on the values, with the lowest value being rank 1, the second-lowest value being rank 2, and so on. If there are ties (same values), assign the average rank to all the tied values.
Theory: 1-7-2-10-4-8-5-3-6-9
Ranks: 1-6-2-10-4-8-5-3-7-9
Practice: 2-8-1-7-3-9-6-5-4-10
Ranks: 2-8-1-7-3-9-6-5-4-10
Step 2: Calculate the difference between the ranks for each pair of data points.
Difference in ranks: 1-(-6)=7, 6-(-8)=14, 2-(-1)=3, 10-(-7)=17, 4-(-3)=7, 8-(-9)=17, 5-(-6)=11, 3-(-4)=7, 7-(-3)=10, 9-(-10)=19
Step 3: Square the differences obtained in Step 2.
Squared differences: 7^2=49, 14^2=196, 3^2=9, 17^2=289, 7^2=49, 17^2=289, 11^2=121, 7^2=49, 10^2=100, 19^2=361
Step 4: Calculate the sum of the squared differences.
Sum of squared differences: 49+196+9+289+49+289+121+49+100+361=1612
Step 5: Use the formula to calculate the Spearman correlation coefficient.
Formula: 1 - (6 * Sum of squared differences) / (n * (n^2 - 1))
Note: n is the number of data points, which in this case is 10.
Spearman correlation coefficient: 1 - (6 * 1612) / (10 * (10^2 - 1))
Calculating the above expression will give you the Spearman correlation coefficient for the given data.
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In the second question regarding the hypothesis test, the decision rule depends on the significance level and the nature of the alternative hypothesis.
The null hypothesis (H0) states that the proportion (p) is equal to 0.50.
The alternative hypothesis (H1) states that the proportion (p) is less than or equal to 0.50.
With a significance level of 0.10, the decision rule can be determined as follows:
A. Reject H0 if the number of successes is 2 or less.
This decision rule suggests that if the number of successes falls within a certain range (2 or less), the null hypothesis should be rejected. However, the specific range is not mentioned in the question.
B. Reject H0 if the number of successes is 8 or more.
This decision rule suggests that if the number of successes falls within a certain range (8 or more), the null hypothesis should be rejected. However, the specific range is not mentioned in the question.
C. Reject H0 if the number of successes is three or less.
This decision rule suggests that if the number of successes falls within a certain range (three or less), the null hypothesis should be rejected.
D. Reject H0 if the number of successes is less than 2 or more than 8.
This decision rule suggests that if the number of successes falls within a certain range (less than 2 or more than 8), the null hypothesis should be rejected. However, the specific range is not mentioned in the question.
Without a specific range mentioned, we cannot definitively determine the correct decision rule. It is important to have the specific range of successes defined in the decision rule for accurate hypothesis testing.