Integrated Natural Science Final Exam Review Workshop Solutions PDF

# Integrated Natural Science - Fall 2024 - Statistics ## Final Exam Review Workshop **December 4, 2024** **Name:** Solutions Please read each question carefully and answer it completely. Please work together. You are encouraged to work together on the white board. Show your work and be able to ex...

# Integrated Natural Science - Fall 2024 - Statistics ## Final Exam Review Workshop **December 4, 2024** **Name:** Solutions Please read each question carefully and answer it completely. Please work together. You are encouraged to work together on the white board. Show your work and be able to explain your reasoning. 1. Use the data set in Table 1 to answer the following questions: * 3, 5, 7, 3, 2, 24, 6, 8, 9, 2, 0 * (a) Find the mean of the data set. 3 + 6 + 7 + 3 + 2 + 24 + 6 + 8 + 9 + 2 + 0 = 66 66 / 11 = 6 * (b) Find the mode of the data set. 2, 3, 5 * (c) Find the median of the data set. 0, 2, 2, 3, 3, 5, 6, 7, 9, 24 med = 5 * (d) Use the 5-number summary to create a box plot for the data set. Be sure to label each quartile with the correct name and value. * Q1 = 2 * Q3 = 7 * med = 5 * (e) Looking at the measures of central tendency that you have calculated, discuss which one does a better job of representing the data. Explain your reasoning. Definitely the median. It is more resistant to the outlier. * (f) What would the z-score be of a data value of 8 for the data set above? Assume a standard deviation of 6.5. z = (x - μ) / σ z = (8 - 6) / 6.5 z = 2 / 6.5 = .31 You are .31 standard deviations above the mean. 2. Which of the measures of central tendency is most resistant to outliers? Why? * **Median** - The outliers are not used to calculate the median. 3. If two data sets have the same range and the same mean, do they always have the same standard deviation? Why or why not? * No: consider **[drawing of histogram]**. ## Descriptive vs. Inferential Statistics What is the difference between descriptive and inferential statistics and give examples of each that were discussed in class. * **Descriptive** - describes a set of data (mean, med, mode, range, std dev) * **Inferential** - tries to infer something about a larger dataset from a sample You want to see if the flavor of cream cheese selected is independent of the type of bagel selected. What statistic would you use? * **Chi-squared test of independence** ## Variance 3. How is the variance related to the standard deviation? * **Variance = (Stdev)**^2 ## Correlation 7. For each of the scatter plots below indicate if it shows a positive correlation, negative correlation, or no correlation. * **[Scatter Plot 1]** - + Correlation * **[Scatter Plot 2]** - No Correlation * **[Scatter Plot 3]** - Negative Correlation ## T-Values 8. If you have 35 data points in one data set and 34 in another. What is the critical t-value at a significance level of p=.05? * df = (35+34)-2 = 67 9. What is the difference between the calculated t-value (sometimes called t-stat) and the critical t-value? How are these used? * **t-value** is what has been calculated. * **t-crit** is on the table and is based on p and df. We compare t-crit and t-value to determine if there is a statistically significant diff between the two. 10. You identify a critical t-value of 2.45. You found a calculated t-value of 2.2. Do you accept or reject the Null Hypothesis? Why? * Accept! Because t-values < t-crit ## Washington State Minimum Wage **WA (1976, 2.30) (2022, 14.49) Fed (1976, 2.30) (2022, 7.25)** In 1976, the minimum wage in Washington State and the federal minimum wage were both $2.30. In 2022, the minimum wage in Washington State is $14.49 and the federal minimum wage is $7.25. Use this information to answer the following questions. * (a) Calculate the average rate of change in federal minimum wage between 1976 and 2022. Write your answer in a sentence. (7.25 - 2.30) / (2022 - 1976) = 4.95 / 46 = 0.11 * The federal min wage increased 11 cents per year between 1976 and 2022. * (b) Calculate the percent rate of change in the federal minimum wage between 1976 and 2022. Write your answer in a sentence. (7.25 - 2.30) / 2.30 = 2.15 * The fed min wga had a 215% increase between 1976 and 2022. * (c) Calculate the average rate of change in the Washington State minimum wage between 1976 and 2022. Write your answer in a sentence. (14.49 - 2.30) / (2022 - 1976) = 12.19 / 46 = 0.265 * The WA min wage increased by 26.5 cents per year between 1976 and 2022. * (d) Calculate the percent rate of change in the Washington State minimum wage between 1976 and 2022. Write your answer in a sentence. (14.49 - 2.30) / 2.30 = 5.3 * The WA min wage had a 530% increase between 1976 and 2022. * (e) In your groups, compare your answers above related to minimum wage above. Does average change or percent change do a better job of communicating the change? Explain your reasoning. * Answers Will Vary. ## Measures of Spread 12. When we are describing a data set, why do we need to include measures of spread as well as measures of central tendency to effectively describe the data? * Answers Will Vary. ## Skewed Distributions 13. If a distribution of scores on an exam was skewed to the right, would more students have received higher scores than if the distribution was skewed to the left? * No. ## Statistical Significance 14. You collect sample of data from plants in two different areas counting the number of lady bugs present. You want to determine if there is a statistically significant difference in the mean number of lady bugs between the two areas. Use this information to answer the following questions: Here are your data: * Area 1: Mean number of lady bugs 35, 12 plants total, standard deviation 2.5. * Area 2: Mean number of lady bugs 47, 14 plants total, standard deviation 3.1. * (a) What is your null hypothesis? There is no significant difference between the number of lady bugs in the different areas. * (b) Would you use a t-test or a chi-square test to evaluate your null hypothesis. Why? T-test. * (c) Hopefully, you selected t-test in the question above, since we have continuous data. * (d) Calculate the t-value for these data. See attached. * (e) Use a p value of .05 and determine if you should accept or reject your null hypothesis. ## Truck, Car, Suv 5. You are curious if buying a truck, car or suv is independent of the color of the vehicle. You collect data and create the following contingency table. Use this table to answer the following questions * **[Contingency Table]** * (a) What is your Null Hypothesis? * (b) Decide which statistical test to use and explain why you chose this test. * (c) Determine if you should accept or reject your null hypothesis. Provide evidence for your decision. * See attached ## Probability with Dice 16. You roll 4 die. What is the probability that die 1 will be a 2, die 2 a 4, die 3 a 1, and die 4 a 6? What is the probability that you will all 4 dice will show a 1? * (1/6)*(1/6)*(1/6)*(1/6) = 0.000772 * The same - all rolls are independent. ## AaBbCcdd & AabbCcDd 17. Parent 1 has a genotype of AABbCcdd and Parent 2 has a genotype of AabbCcDd. What is the probability that their offspring will have the genotype AabbCcdd? * 1 / 16 18. Parent 1 has a genotype of AABbCcdd and Parent 2 has a genotype of AabbCcDd. What is the probability that their offspring will have the genotype AabbCcdd or AABbccDd? * 3 / 32