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A Level Statistics Quiz 1

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  • Why is the area under the normal curve equal to 1?
    Because it represents the total probability of all outcomes.
  • What does it mean to “reject the null hypothesis”?
    here is sufficient evidence to support the alternative hypothesis.
  • 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.
  • Name two conditions for using a binomial distribution model.
    Fixed number of trials and constant probability of success; outcomes are independent.
  • Give one assumption necessary for modelling data with a normal distribution.
    The data must be symmetrically distributed around the mean.
  • 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 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 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.
  • Why is the interquartile range often preferred over the range?
    It is not affected by extreme values or outliers.
  • What does a large standard deviation tell us about a data set?
    That the data points are more spread out from the mean.
  • 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.
  • 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).
  • 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 does a strong correlation not imply causation?
    There may be lurking variables or the relationship could be coincidental.
  • 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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