Can you create all theoretical questions on statistics Zimsec possible questions

Here are some possible theoretical questions on Statistics relevant to the Zimsec A-level curriculum:

• Define the terms population, sample, parameter, and statistic. Explain the relationship between them.
• Distinguish between primary data and secondary data, providing an example for each. State one advantage and one disadvantage of using secondary data.
• Describe three different methods of random sampling, explaining the procedure for each and stating one advantage and one disadvantage of each method.
• Explain what is meant by sampling bias and give two examples of how it can arise in a statistical investigation.
• Define the terms qualitative variable and quantitative variable. Further classify quantitative variables into discrete and continuous, providing an example for each.
• Discuss the advantages and disadvantages of using the mean, median, and mode as measures of central tendency.
• Explain the concept of variance and standard deviation as measures of dispersion. Why is standard deviation often preferred over variance in practical applications?
• State the axioms of probability.
• Define mutually exclusive events and independent events. Provide an example to illustrate the difference between them.
• State the conditions under which a random variable can be modelled by a Binomial distribution.
• State the conditions under which a random variable can be modelled by a Poisson distribution.
• Describe the key properties of the Normal distribution. Explain the significance of its mean and standard deviation.
• Explain the circumstances under which the Normal distribution can be used as an approximation to the Binomial distribution, and state the necessary conditions for this approximation.
• Explain the circumstances under which the Normal distribution can be used as an approximation to the Poisson distribution, and state the necessary conditions for this approximation.
• Define the terms null hypothesis ($\text{H}_0$) and alternative hypothesis ($\text{H}_1$) in the context of hypothesis testing.
• Explain what is meant by a Type I error and a Type II error in hypothesis testing. Discuss the implications of each type of error.
• Define the level of significance ($\alpha$) in hypothesis testing. How does it relate to the critical region?
• Explain the concept of a p-value in hypothesis testing and how it is used to make a decision about the null hypothesis.
• Distinguish between correlation and causation. Provide an example where correlation does not imply causation.
• Explain the meaning of the coefficient of determination ($\text{R}^2$) in linear regression.
• Define what an index number is and explain its purpose. Distinguish between a Laspeyres price index and a Paasche price index.