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A Level Statistics Quiz 1
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What does the expected value of a random variable represent in practical terms?
The long-run average outcome if the experiment is repeated many times.
What is the key difference between discrete and continuous probability distributions?
Discrete variables take specific values; continuous variables can take any value within a range.
Why is it important to evaluate whether a model’s assumptions hold in real-life data?
Because if the assumptions are invalid, the model may give misleading results.
What is meant by the critical region in hypothesis testing?
The set of values of the test statistic that would lead to rejecting the null hypothesis.
Why is it inappropriate to use a regression line to make predictions outside the range of the data?
It assumes the same trend continues, which may not be valid (extrapolation risk).
Why does a strong correlation not imply causation?
There may be lurking variables or the relationship could be coincidental.
What does it mean to “reject the null hypothesis”?
here is sufficient evidence to support the alternative hypothesis.
What does a p-value represent in hypothesis testing?
he probability of obtaining the observed result (or more extreme) assuming the null hypothesis is true.
Name two conditions for using a binomial distribution model.
Fixed number of trials and constant probability of success; outcomes are independent.
Why is the area under the normal curve equal to 1?
Because it represents the total probability of all outcomes.
Give one assumption necessary for modelling data with a normal distribution.
The data must be symmetrically distributed around the mean.
What does a large standard deviation tell us about a data set?
That the data points are more spread out from the mean.
Why is the interquartile range often preferred over the range?
It is not affected by extreme values or outliers.
What is the difference between qualitative and quantitative data?
Qualitative data is descriptive (e.g. colours), while quantitative data is numerical (e.g. heights).
Why might a random sample be preferred over a convenience sample in statistical analysis?
A random sample reduces bias and is more representative of the population.
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