The document provided is a summative assessment for a Business Statistics course with a multiple-choice format. Below are a few detailed steps to help tackle some of the statistical questions presented in the assessment:

1. Identifying Variable Types (Question 1):

   • To determine whether a variable is discrete or continuous and its level of measurement, consider if the data can take on distinct separate values (discrete) or any value within a range (continuous). For example, counting occurrences is often discrete (like noise disturbances), while measurements like temperature are continuous.

2. Understanding Sampling (Questions 4, 6, 7):

   • For stratified sampling, the population is divided based on a characteristic, and random samples are drawn from each subgroup. Convenience sampling, by contrast, involves choosing the most easily accessible samples, as noted in the agriculturalist example.

3. Probability and Normal Distribution (Questions 15, 17, 18):

   • Probability questions with normally distributed data can often be addressed using Z-scores to find cumulative probabilities. For example, to find the likelihood of consuming less than 270 kWh with a mean of 284 and standard deviation of 34, calculate the Z-score and reference a Z-table.

4. Linear Regression Interpretation (Questions 23–25):

   • Linear regression equations like $\hat{y} = a + bx$ can help predict values given certain inputs, such as predicting class marks based on class size. The correlation coefficient measures the strength and direction of this linear relationship, with values near $\pm1$ indicating a strong relationship.

5. Coefficient of Variation (Question 9):

   • The Coefficient of Variation (CV) is calculated as $\frac{\text{standard deviation}}{\text{mean}} \times 100\%$ and helps compare variability across different datasets.

Would you like solutions for specific questions, a breakdown of the formulas needed, or help with probability tables? Let me know how I can support you further!

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Related Practice Questions

1. How can you differentiate between a population parameter and a sample statistic?
2. What are the benefits of using stratified sampling over simple random sampling?
3. How would you interpret a correlation coefficient of -0.8?
4. Calculate the probability of exactly two events occurring if the average rate is four events per time period.
5. How does the coefficient of variation help compare datasets with different units?

Tip: When unsure about the normal distribution, always check if the problem provides mean and standard deviation, as these allow for Z-score calculation to find probabilities.