# Spring 2022 Midterm Test Solutions for Inferential Statistics and Statistical Analysis- The University of Arizona

Explore the below test questions and solutions done as a midterm test in the spring of 2022 at the University of Arizona. The test covers questions that our statistical analysis exam writing service helped different students complete and answers to help you revise and prepare for your tests. If you need help with your coursework, you can contact our team and we will help you complete your statistics exams. Check out our blog to see how our experts answered the test questions, and learn how to do it yourself in future tests.

## Exam Question 1: Provide a definition for Weighted Mean (0.50 points)

**Exam Solution:** Weighted mean is the weighted average where some data points are weighed more than others. For a situation where all the weights assigned are equal, the simple mean is equal to the weighted mean.

## Exam Question 2: Calculate a weighted mean for data concerning Buying a Camera and explain what camera you would purchase.

Here is the data set to use for your weighted mean calculation:

The average consumer rating for two cameras is comprised of Image Quality (I), Battery Life (B), and Zoom Range (Z). The information for both brand A and B are below:

Brand A – I = 8; B = 6; Z = 7

Brand B – I = 9; B = 8; Z = 3

The weighting for these features is I = 50%, B = 30%, Z = 20%. This is not your personal rating but the weighting you will use in the calculation of what brand to buy.

**Exam Solution:
**

Weighted mean for Brand A = 8*0.5 + 6*0.3 + 7*0.2 = 4+1.8+1.4 = 7.2

Weighted mean for Brand B = 9*0.5 + 8*0.3 + 3*0.2 = 4.5+2.4+0.6 = 7.5

Since the weighted average for Brand B is higher, I will purchase Brand B camera.

## Exam Question 3: Speculate on how you could use Inferential Statistics in your future employment

**Exam Solution: **Inferential statistics can be used to identify if there is any difference in the pay scale of the different companies in the field. Using the pay scale data for the different companies in my field, ANOVA can be used to find out any such differences. Regression analysis, another inferential statistic, can be used to see which variables are more significant predictors of getting hired in a particular company/sector. We may use data on education, experience, etc for such analysis.

## Exam Question 4: Explains what Statistical Significance is (0.75 points).

**Exam Solution: **If the results are statistically significant, this means that the likelihood of the existence of a relationship does not exist by chance. Usually, the value in statistical significance is compared to the alpha-level value. If the p-value of the hypothesis is less than the alpha level, the results are statistically significant. This means that the likelihood of the existence of a relationship does not exist by chance. However, if the p-value of the hypothesis is greater than the alpha level, the results are not considered to be statistically significant. This means that the likelihood of the existence of a relationship exists by chance.

## Exam Question 5: Explain what a Pearson r calculation tells one about the data (0.75 points)

**Exam Solution: **Pearson r is the correlation between the two variables. There are two parts of the Pearson r: its magnitude and direction. The positive or negative sign of the Pearson r tells us about the direction of correlation between the two variables. If the value is positive, it means that an increase in one of the variables results in an increase in the other variable and vice versa. However, if the value is negative, it means that an increase in one of the variables results in a decrease in the other variable and vice versa. The other part of Pearson r is its magnitude. The magnitude of the correlation coefficient tells us about the strength of the relationship. The value of r lies between -1 and 1. The closer is the value to 1 or -1, the stronger is the relationship between the two variables. However, the closer is the value to zero, the weaker is the relationship.