Preparing for the next class
In the next class, you will need to be able to calculate the mean and standard deviation of a variable, create a histogram, and describe the shape and spread of a histogram. You will also need to describe null and alternative hypotheses and identify the difference between one-tailed and two-tailed hypothesis tests.
For Questions 1–4: Use the DCMP Describing and Exploring Quantitative Variables tool at https://dcmathpathways.shinyapps.io/EDA_quantitative/ and select the dataset “CO2 Emissions of EU Countries” to answer the following questions.
Question 1
1) What is the mean per capita CO2 emission of European Union (EU) countries?
a) 28 metric tons
b) 3.6 metric tons
c) 7.86 metric tons
d) 3.61 metric tons
Question 2
2) What is the standard deviation of per capita CO2 emissions of EU countries?
a) 28 metric tons
b) 3.6 metric tons
c) 7.86 metric tons
d) 3.61 metric tons
Question 3
3) Create a histogram of per capita CO2 emissions of EU countries. Is there a possible outlier in the dataset?
a) Yes
b) No
Question 4
4) Which of the following statements is correct about the shape and spread of the histogram of per capita CO2 emissions of EU countries?
a) The distribution of per capita CO2 emissions of EU countries is skewed. The center of the data is around 7–8 metric tons, and most of the data are between about 3 metric tons to about 14 metric tons.
b) The distribution of per capita CO2 emissions of EU countries is approximately normal. The center of the data is around 5 metric tons, and most of the data are between 3 metric tons to about 14 metric tons.
c) The distribution of per capita CO2 emissions of EU countries is skewed towards the left. The center of the data is around 10 metric tons, and most of the data are between 2 metric tons to 20 metric tons.
Question 5
5) The process of hypothesis testing starts with the assumption that ____.
a) the null hypothesis is true
b) the null hypothesis is false
c) the alternative hypothesis is true
d) the null and alternative hypotheses are true
Question 6
6) Which of the following represents a two-tailed hypothesis?
a) [latex]p_{1}-p_{2}\neq0[/latex]
b) [latex]p_{1}-p_{2}<0[/latex] c) [latex]p_{1}-p_{2}>0[/latex]
d) [latex]p_{1}-p_{2}\ge0[/latex]
Question 7
7) Which of the following represents a one-tailed hypothesis test where the population proportion for Sample 1 ([latex]p_{1}[/latex]) is larger than the population proportion for Sample 2 ([latex]p_{2}[/latex])?
a) [latex]p_{1}-p_{2}\neq0[/latex]
b) [latex]p_{1}-p_{2}<0[/latex] c) [latex]p_{1}-p_{2}>0[/latex]
d) [latex]p_{1}-p_{2}\ge0[/latex]
Question 8
8) Determine whether this statement is true or false: The alternative hypothesis states that there is no difference/no effect.
a) True
b) False
Question 9
9) In the next in-class activity, you will be introduced to the two assumptions that are needed for hypothesis tests for means:
- The first assumption is a random sample from the population of interest.
- The second assumption is a normal population distribution or large sample size.
Write down these assumptions in your notebook and have them ready to use in class.