Practice questions

• Univariate analysis: The data which is being analysed contains one variable. For example, analysing the customers visiting an e-commerce fashion website. The data can be divided into men, women and kids, as following:

  Category	Number per hour
  Women	78
  Men	49
  Kids	12

  The major purpose of this analysis is to describe and find patterns in data.

• Bivariate analysis: It is used to find relationships between two different variables. For example, finding the relationship between Employee satisfaction level and income.
• Multivariate analysis: It is the analysis of three or more variables. For example, analyse the factors that could have affected the lower sales of a newly launched product.

The power of a statistical test is inversely proportional to the probability of making a Type-2 error ($\beta$); so, it is equal to $1 - \beta$. More…

• In stratified random sampling, the whole population is divided into strata based on common characteristics. Then, certain elements are selected from each stratum.
• On the other hand, in cluster sampling, the whole population is divided into clusters, and then some of the clusters are chosen randomly to create a sample.

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• When you perform a statistical test a p-value helps you determine the significance of your results in relation to the null hypothesis.
• The level of statistical significance is often expressed as a p-value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.
• The advantage of p-value approach is that you do not need to state the confidence level ahead of solving the hypothesis, as it becomes difficult to determine the confidence level in any particular situation.

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Let’s assume that the data is normally distributed. In a normal distribution:

• 68% of the data lies between one standard deviations
• 95% of the data lies between two standard deviations, and
• 99.7% of the data lies between three standard deviations

Therefore only 5% of the data will remain unaffected. More…

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Testing the alternate versions of websites is important in digital marketing, search engine optimisation etc. By testing the alternate versions of a website, A/B testing enables data-driven decision-making instead of making decisions based on simple gut feeling. For example, an e-commerce company that sells multiple products on its website wanted to increase its sales on its website. To increase the sales, they used A/B testing. They changed the ‘Buy Now’ button to ‘Shop Now’, and this drove 17% more people to click on that button. This dealt a significant impact on the revenue of the company. So, this is an example of how a small change can produce significant results for a business and why A/B testing is very important. More…

• Z-test: It is used to test the hypothesis when the population data is normally distributed and the following conditions are met:
  • Condition 1: n > 30, which means that the population sample size should be greater than 30 observations
  • Condition 2: 𝝈 is known, i.e. the population standard deviation is known
• T-test: It is used to test the hypothesis when the population data is normally distributed and the following conditions are met:
  • Condition 1: n < 30, which means that the population sample size should be less than 30 observations
  • Condition 2: 𝝈 is not known, i.e. the population standard deviation is unknown
• Chi-square test: This test is used to determine if there is a significant relationship between two nominal (categorical) variables.
• F-test: F-test is used to test the hypothesis on the equality of two population variances.

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• In cluster sampling, the whole population is divided into clusters, and then some of the clusters are chosen randomly to create a sample.
• Whereas in systematic sampling, a starting point is selected in the population, and then, the elements are selected at regular, fixed intervals to create a sample.

A confidence interval of 95% signifies the range of values within which you can be 95% confident that the mean will lie in that range of values.

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It is a value calculated from the sample data that is used to evaluate the strength of evidence in support of a null hypothesis. For example, if the test statistic in a hypothesis test is equal to ‘A’ and the probability of observing the test statistic ‘A’ is less than the significance level, the null hypothesis is rejected.

• Mean and expected values are the same but are used in different contexts.
• We take the mean value in the context of probability distribution or samples,
• and we take the expected value in the context of random variables.