Activity 12- Statistics Exercise V

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Jan 9, 2024

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#1. What information does a correlation coefficient convey? A correlation coefficient is a measure, ranging from r=-1.0 to r=+1.0. When the value is closer to +/-1.0 a stronger correlation is indicated. The correlation coefficient also indicates the direction of the slope of the correlation. The Pearson correlation coefficient measures the strength and direction for the relationship between two factors and each factor is on an interval or ratio scale of measurement. The Spearman correlation coefficient measures the strength and direction of the linear relationship between two factors, each factor is ranked on an ordinal scale of measurement. #2. State whether each of the following is an example of a positive correlation or a negative correlation. 1. Higher education level is associated with a larger annual income. - Positive correlation, education level is an ordinal variable and annual income is ratio variable. When one variable increase, so will the second variable. This is a Spearman’s correlation because it contains one ordinal variable and one ratio variable. 2. Increased testosterone is associated with increased aggression. - Positive correlation, testosterone is a ratio variable and aggression are an interval, which is an example of a Pearson’s correlation. Again, if one variable increases, the second variable follows or increases as well. 3. The smaller the class size, the more students believe they are receiving a quality education. - Negative correlation, we want to know if there is a correlation between a small class (ratio) and the quality of education (interval). Implying that as one variable increases the other decreases. This example represents a Pearson’s correlation. 4. Rising prices of apples are associated with the sale of fewer apples. - Negative correlation, we are considering if increased price of apples (ratio) is related to the sale of less apples (ratio). Similar to the last problem, if one variable increases, the other decrease and again is an example of Pearson’s correlation. #3. Which is the predictor variable ( X ) and which is the criterion variable ( Y ) for each of the following examples? 1. A researcher tests whether the size of an audience can predict the number of mistakes a student makes during a classroom presentation. - X – Audience size, Y – Number of mistakes

2. A military officer tests whether the duration of an overseas tour can predict the morale among troops overseas. - X – Tour duration, Y – Troop morale 3. A social psychologist tests whether the size of a toy in cereal boxes can predict preferences for that cereal. - X – Toy size, Y – Cereal preference #4. d. HAPPY = 4.47 - .018L A regression equation is used to predict the value of one variable, such as relationship happiness based on the second variable, lifestyle. The SPSS output labeled coefficients provides us with the necessary information to determine if the variable lifestyle contributes to the equation being statistically significant. The column labeled unstandardized coefficients B shows the y-intercept of the regression line (constant, 4.47) and the slope of the regression line (lifestyle, -.02). To determine whether a regression equation can significantly predict variance in y, the regression variation of happiness and is not related to change in the predictor variable, lifestyle. F= MSregression/MSresidual .004=.02/4.47 When looking at the sig. or the p-value for lifestyle you can see that a sig. of .004 is less than alpha .05, which suggests that the regression model is indeed statistically significant.

#5. b. People who want a more luxurious lifestyle tend to be more financially dependent. Let’s take a look at the SPSS data table labeled correlations. We want to know if lifestyle and dependency are correlated. We will utilize the sig. (2- tailed) column under the dependency column to determine if the test is statistically significant in other terms, lifestyle and dependency correlate with one another. As we can see the sig. (2-tailed) is .000, which is less then alpha .05. This tells us that our results are statistically significant and tells us that there is a correlation between lifestyle and dependency. We can now utilize the R-value labeled on the table Pearson’s Correlation .321 to determine if there is a positive or negative correlation. .321 is a positive number and closer to R=+1, which tells us that there is a positive correlation. This leads us to our final answer that people who want a more luxurious lifestyle tend to be more financially dependent.

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#6. d. .822 The SPSS date output labeled correlations shows us that the Pearson Correlation (R) is .822. We also want to determine if there is a positive or negative relationship. With R being .822 we can determine there is a positive linear relationship. This can be determined because .822 is a positive number and is closest to R=+1. If our R value was negative, then we would determine there is a negative linear relationship. Because we know the relationship is positive, we also know that as the participants age increase so does the partner’s age. #7. a. The relationship is non-significant.

The SPSS data output labeled Correlations gives us a p-value of .06. Based on a standard alpha level of .05 we can determine that our p-value is greater than .05, which tells us that the result is not statistically significant. Also put, the correlation between risk taking and relationship happiness is not significant. This provides us with our final answer that the relationship is not significant. #8. If you randomly chose someone from this sample, what is the chance that they described their relationship as either Happy or Very Happy? d. 69% To determine the chances of describing a relationship as either happy or very happy you would want to determine the frequency of happy and very happy. Let’s look at the SPSS data output labeled relationship happiness. We will be utilizing the percentage column and adding happy and very happy.

37.0 + 32.3 = 69.3 Rounded to 69%

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