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What is the difference between descriptive and inferential statistics and give examples of each that were discussed in class?
What is the difference between descriptive and inferential statistics and give examples of each that were discussed in class?
Descriptive statistics describes a set of data (mean, median, mode). Inferential statistics tries to infer something about a larger dataset from a smaller dataset.
You want to see if the flavor of cream cheese selected is independent of the type of bagel selected.
What statistic would you use?
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
How is the variance related to the standard deviation?
How is the variance related to the standard deviation?
Variance = (Standard Deviation)^2
For each of the scatter plots below indicate if it shows a positive correlation, negative correlation, or no correlation.
For each of the scatter plots below indicate if it shows a positive correlation, negative correlation, or no correlation.
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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?
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?
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What is the difference between the calculated t-value (sometimes called t-stat) and the critical t-value? How are these used?
What is the difference between the calculated t-value (sometimes called t-stat) and the critical t-value? How are these used?
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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?
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?
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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.
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.
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(b) Calculate the percent rate of change in the federal minimum wage between 1976 and 2022. Write your answer in a sentence.
(b) Calculate the percent rate of change in the federal minimum wage between 1976 and 2022. Write your answer in a sentence.
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(c) Calculate the average rate of change in the Washington State minimum wage between 1976 and 2022. Write your answer in a sentence.
(c) Calculate the average rate of change in the Washington State minimum wage between 1976 and 2022. Write your answer in a sentence.
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(d) Calculate the percent rate of change in the Washington State minimum wage between 1976 and 2022. Write your answer in a sentence.
(d) Calculate the percent rate of change in the Washington State minimum wage between 1976 and 2022. Write your answer in a sentence.
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(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.
(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.
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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?
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?
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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?
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?
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You collect a 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?
You collect a 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?
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(b) Would you use a t-test or a chi-square test to evaluate your null hypothesis. Why?
(b) Would you use a t-test or a chi-square test to evaluate your null hypothesis. Why?
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(c) Hopefully, you selected t-test in the question above, since we have continuous data. (d) Calculate the t-value for these data.
(c) Hopefully, you selected t-test in the question above, since we have continuous data. (d) Calculate the t-value for these data.
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(e) Use a p value of .05 and determine if you should accept or reject your null hypothesis.
(e) Use a p value of .05 and determine if you should accept or reject your null hypothesis.
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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 truck car suv
red 12 6 2
white 20 24 8
gray 3 18 20 (a) What is your Null Hypothesis?
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 truck car suv red 12 6 2 white 20 24 8 gray 3 18 20 (a) What is your Null Hypothesis?
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(b) Decide which statistical test to use and explain why you chose this test.
(b) Decide which statistical test to use and explain why you chose this test.
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(c) Determine if you should accept or reject your null hypothesis. Provide evidence for your decision.
(c) Determine if you should accept or reject your null hypothesis. Provide evidence for your decision.
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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?
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?
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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?
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?
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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?
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?
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What is the median of the data set 3, 5, 7, 3, 2, 24, 6, 8, 9, 2, 0?
What is the median of the data set 3, 5, 7, 3, 2, 24, 6, 8, 9, 2, 0?
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Which measure of central tendency is least affected by outliers?
Which measure of central tendency is least affected by outliers?
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What is the z-score for a data value of 8 given a mean of 6 and a standard deviation of 6.5?
What is the z-score for a data value of 8 given a mean of 6 and a standard deviation of 6.5?
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Which of the following best describes the relationship between variance and standard deviation?
Which of the following best describes the relationship between variance and standard deviation?
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If two data sets have the same range and mean, what can be inferred about their standard deviations?
If two data sets have the same range and mean, what can be inferred about their standard deviations?
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Which statistic would be appropriate to test if the flavor of cream cheese is independent of the type of bagel?
Which statistic would be appropriate to test if the flavor of cream cheese is independent of the type of bagel?
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How is the mode defined in a data set?
How is the mode defined in a data set?
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Which of the following data attributes does NOT contribute to calculating the five-number summary?
Which of the following data attributes does NOT contribute to calculating the five-number summary?
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What is the average rate of change in the federal minimum wage between 1976 and 2022?
What is the average rate of change in the federal minimum wage between 1976 and 2022?
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What is the percent rate of change in the federal minimum wage between 1976 and 2022?
What is the percent rate of change in the federal minimum wage between 1976 and 2022?
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What is the average rate of change in the Washington State minimum wage between 1976 and 2022?
What is the average rate of change in the Washington State minimum wage between 1976 and 2022?
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What was the percent rate of change in the Washington State minimum wage from 1976 to 2022?
What was the percent rate of change in the Washington State minimum wage from 1976 to 2022?
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What does the t-value represent in hypothesis testing?
What does the t-value represent in hypothesis testing?
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If a critical t-value is 2.45 and the calculated t-value is 2.2, what action should be taken regarding the Null Hypothesis?
If a critical t-value is 2.45 and the calculated t-value is 2.2, what action should be taken regarding the Null Hypothesis?
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Why are measures of spread essential when describing a data set along with measures of central tendency?
Why are measures of spread essential when describing a data set along with measures of central tendency?
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What can lead you to consider using a t-test in data analysis?
What can lead you to consider using a t-test in data analysis?
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What is the appropriate statistical test to determine if there is a significant difference in the mean number of lady bugs between two areas?
What is the appropriate statistical test to determine if there is a significant difference in the mean number of lady bugs between two areas?
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If the probability of rolling a specific sequence with four dice is $ rac{1}{6}^4$, what is the probability of rolling four ones?
If the probability of rolling a specific sequence with four dice is $ rac{1}{6}^4$, what is the probability of rolling four ones?
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What is the null hypothesis when determining the independence of vehicle type and color?
What is the null hypothesis when determining the independence of vehicle type and color?
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What is the expected outcome of rejecting the null hypothesis concerning the number of lady bugs in the two areas?
What is the expected outcome of rejecting the null hypothesis concerning the number of lady bugs in the two areas?
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If the offspring of two parents have a probability of $1/16$ for the genotype AabbCcdd, what does this indicate about gene inheritance?
If the offspring of two parents have a probability of $1/16$ for the genotype AabbCcdd, what does this indicate about gene inheritance?
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What is implied when the mean number of lady bugs in Area 1 is 35 and in Area 2 is 47?
What is implied when the mean number of lady bugs in Area 1 is 35 and in Area 2 is 47?
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What is the important characteristic of a contingency table relevant for hypothesis testing?
What is the important characteristic of a contingency table relevant for hypothesis testing?
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In genetic probability, if the probability of having the genotype AabbCcdd or AABbccDd is $3/32$, what can be inferred?
In genetic probability, if the probability of having the genotype AabbCcdd or AABbccDd is $3/32$, what can be inferred?
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Study Notes
Statistics Review
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Data Set: 3, 5, 7, 3, 2, 24, 6, 8, 9, 2, 0
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Mean Calculation: Sum of values (3+5+7+3+2+24+6+8+9+2+0) = 72; Divided by count (11) = 6.55
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Mode: Value occurring most frequently: 2
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Median: Middle value when ordered: 5
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5-Number Summary: Required to create a box plot
- Minimum: 0
- Q1 (First Quartile): 2
- Median: 5
- Q3 (Third Quartile): 8
- Maximum: 24
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Central Tendency:
- Median is resistant to outliers - less affected by extreme values.
- Mean is not as resistant and may provide less true representation of data.
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Z-Score: The formula is calculated. For a data value of 8, the z-score is 0.31.
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Resistant Measure: The median is most resistant to outliers; outliers do not affect the median calculation.
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Standard Deviation & Range: Data sets with the same mean and range may not have same standard deviation; standard deviation takes into account spread, or variation of the data set.
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Significance Level (p=.05). Used in hypothesis testing.
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Critical T-value. The critical t-value corresponds to the chosen significance level (e.g., p=0.05), the degrees of freedom (related to sample size), and the direction of the test, to reject or accept null hypothesis.
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t-value and Critical t-value: Calculating and comparing these two values help make decision regarding statistical significance of the collected data.
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Null Hypothesis: Asserts that there is no significant difference or relationship present between variables, or that variables is independent of each other.
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Contingency Table: Used for determining if the relationship between categories is random, or has some meaningful relationship.
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Probability Calculation: Using combinations and permutations to determine likelihood of an event in multiple dice rolls, and from parental genotype.
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Description
Test your understanding of key statistical concepts such as mean, mode, median, and outliers. This quiz covers central tendency, z-scores, and standard deviation based on the provided data set. Prepare to enhance your statistical analysis skills!
