Statistics Review Quiz

What is the difference between descriptive and inferential statistics and give examples of each that were discussed in class?

You want to see if the flavor of cream cheese selected is independent of the type of bagel selected. What statistic would you use?

How is the variance related to the standard deviation?

For each of the scatter plots below indicate if it shows a positive correlation, negative correlation, or no correlation.

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?

What is the difference between the calculated t-value (sometimes called t-stat) and the critical t-value? How are these used?

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?

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.

(b) Calculate the percent rate of change in the federal 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.

(d) Calculate the percent rate of change in the Washington State minimum wage between 1976 and 2022. Write your answer in a sentence.

(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.

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?

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?

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?

(b) Would you use a t-test or a chi-square test to evaluate your null hypothesis. Why?

(c) Hopefully, you selected t-test in the question above, since we have continuous data. (d) Calculate the t-value for these data.

(e) Use a p value of .05 and determine if you should accept or reject 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?

(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.

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?

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 or AABbccDd?

What is the median of the data set 3, 5, 7, 3, 2, 24, 6, 8, 9, 2, 0?

Which measure of central tendency is least affected by outliers?

What is the z-score for a data value of 8 given a mean of 6 and a standard deviation of 6.5?

Which of the following best describes the relationship between variance and standard deviation?

If two data sets have the same range and mean, what can be inferred about their standard deviations?

Which statistic would be appropriate to test if the flavor of cream cheese is independent of the type of bagel?

How is the mode defined in a data set?

Which of the following data attributes does NOT contribute to calculating the five-number summary?

What is the average 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?

What is the average rate of change in the Washington State minimum wage between 1976 and 2022?

What was the percent rate of change in the Washington State minimum wage from 1976 to 2022?

What does the t-value represent in hypothesis testing?

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?

Why are measures of spread essential when describing a data set along with measures of central tendency?

What can lead you to consider using a t-test in data analysis?

What is the appropriate statistical test to determine if there is a significant difference in the mean number of lady bugs between two areas?

If the probability of rolling a specific sequence with four dice is $rac{1}{6}^4$, what is the probability of rolling four ones?

What is the null hypothesis when determining the independence of vehicle type and color?

What is the expected outcome of rejecting the null hypothesis concerning the number of lady bugs in the two areas?

If the offspring of two parents have a probability of $1/16$ for the genotype AabbCcdd, what does this indicate about gene inheritance?

What is implied when the mean number of lady bugs in Area 1 is 35 and in Area 2 is 47?

What is the important characteristic of a contingency table relevant for hypothesis testing?

In genetic probability, if the probability of having the genotype AabbCcdd or AABbccDd is $3/32$, what can be inferred?

Mean

Mode

Median

Outlier

Median - Outlier resistance

5-Number Summary

Box Plot

Z-score

Descriptive Statistics

Inferential Statistics

Chi-Square Test

Variance

Standard Deviation

Positive Correlation

Negative Correlation

No Correlation

T-value

T-critical

Null Hypothesis

Degrees Of Freedom (df)

Probability

Average Change

Percent Change

Resistant to outliers

Standard Deviation vs. Variance

Scatter Plot: + Correlation

Scatter Plot: - Correlation

Scatter Plot: No Correlation

Accept or Reject Null?

Average Rate of Change

Percent Rate of Change

Measures of Spread

Skewed Distributions

Why Measures of Spread?

Right Skewed Distribution

Left Skewed Distribution

T-test

Contingency Table

Independent Events

Genotype Probability