“Cracking the Stats Interview: Common Questions and How to Ace Them”

Two types of questions ask in interview

Theoretical Questions

Numerical Questions

Theoretical Questions

Explain confidence interval in simple words.

A confidence interval is a statistical measure that helps us estimate the range of values where the true population parameter (such as the mean or proportion) is likely to lie with a certain degree of confidence based on a sample of data.

For example, if we want to estimate the average height of all people in a country, we can take a sample of people and calculate the sample mean. However, we cannot be sure that the sample mean is exactly equal to the true population mean. The confidence interval gives us a range of values where the true population mean is likely to fall within, based on our sample.

If we know the population standard deviation:

Confidence Interval = Sample Mean ± Z* (Population Standard Deviation / sqrt(n))

If we don't know the population standard deviation:

Confidence Interval = Sample Mean ± t* (Sample Standard Deviation / sqrt(n))

"Understanding Confidence Intervals: A Beginner's Guide"

Population Vs Sample Population:medium.com

Numerical Questions

1. let say we have a sample size of n . the margin of error for our sample size is 3 .How many more samples would we need to decrease the margin of error to 0.3

To calculate how many more samples we would need to decrease the margin of error from 3 to 0.3, we can use the formula:

M=z*sigma/sqrt(n)

n2 = (n1 / (M2 / M1)²)

where:

n1 is the initial sample size

M1 is the initial margin of error (3 in this case)

M2 is the desired margin of error (0.3 in this case)

n2 is the new sample size we need to achieve the desired margin of error

Plugging in the values we have:

n2 = (n1 / (M2 / M1)²) = (n1 / (0.3 / 3)²) = (n1 / 0.01) = 100n1

Therefore, we would need 100 times more samples than our initial sample size to decrease the margin of error from 3 to 0.3.

2. Three zebras are chilling in the desert. Suddenly a lion attack. Each zebra is sitting on a corner of an equally length triangle. Each zebra randomly picks a direction and only runs along the outline of the triangle to either edge of triangle. what is the probability that none of the zebras collide?

We can approach this problem by first considering the probability that the first zebra chooses a direction that does not lead to collision, then the probability that the second zebra chooses a direction that also does not lead to collision given the first zebra's choice, and finally the probability that the third zebra also chooses a direction that does not lead to collision given the choices of the first two zebras.

Let's assume that the triangle has a side length of 1 unit, and label the corners of the triangle as A, B, and C.

Without loss of generality, let's assume that the first zebra chooses corner A and runs to either B or C. This means that the second zebra can choose one of the two remaining corners, either B or C. If the first zebra runs to corner B, then the second zebra must choose corner C, and vice versa. In this case, the zebras will not collide only if the third zebra chooses the corner that is opposite to the direction that the second zebra runs. For example, if the first zebra runs from A to B and the second zebra runs from B to C, then the third zebra must choose corner A in order to avoid collision.

The probability that the first zebra chooses a direction that does not lead to collision is 1, since it can choose either corner B or C with equal probability. The probability that the second zebra also chooses a direction that does not lead to collision given the first zebra's choice is 1/2, since there is only one remaining corner that leads to no collision out of two possible choices. Finally, the probability that the third zebra chooses a direction that does not lead to collision given the choices of the first two zebras is 1/2, since there is only one remaining corner that leads to no collision out of two possible choices.

Therefore, the probability that none of the zebras collide is:

1 x 1/2 x 1/2 = 1/4

So the probability that none of the zebras collide is 1/4 or 0.25.

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Here are some common theoretical interview questions related to statistics in data science:

What is the difference between a population and a sample?

What is the central limit theorem and why is it important?

What is the law of large numbers and how does it relate to the central limit theorem?

What is the difference between a parametric and non-parametric test?

What is the difference between Type I and Type II errors?

What is p-value and how is it used in hypothesis testing?

What is the difference between correlation and causation?

What is the difference between a confidence interval and a prediction interval?

What is overfitting and how can it be prevented?

What is regularization and how does it help with overfitting?

1. What is the difference between a population and a sample?

A population is the entire group of individuals or objects that we are interested in studying, while a sample is a subset of the population that we actually collect data from. The population is usually much larger than the sample, and it is often impractical or impossible to collect data from every individual in the population. Therefore, we use statistical techniques to infer information about the population based on the data collected from the sample.

2. what is the central limit theorem and why is it important?

The central limit theorem states that for large sample sizes, the sampling distribution of the sample means will be approximately normal, regardless of the underlying distribution of the population. In other words, as we increase the sample size, the distribution of sample means will tend to approach a normal distribution, even if the population distribution is not normal. This is important because many statistical methods and hypothesis tests rely on the assumption of normality, and the central limit theorem allows us to use these methods even when the population distribution is unknown or non-normal.

3. What is the law of large numbers and how does it relate to the central limit theorem?

The law of large numbers (LLN) is a theorem that states that as the sample size gets larger, the sample mean will converge to the population mean. The LLN is related to the CLT because the CLT assumes that the sample size is large enough for the sample mean to be normally distributed, and the LLN tells us that as the sample size gets larger, the sample mean will become a better and better estimate of the population mean.

4. What is the difference between a parametric and non-parametric test?

A parametric test is a statistical test that makes assumptions about the underlying distribution of the data, such as assuming that the data follows a normal distribution. Examples of parametric tests include t-tests and ANOVA. A non-parametric test, on the other hand, does not make any assumptions about the underlying distribution of the data. Non-parametric tests are often used when the data is not normally distributed or when the sample size is small. Examples of non-parametric tests include the Wilcoxon rank-sum test and the Kruskal-Wallis test.

5. What is the difference between Type I and Type II errors?

Type I error occurs when we reject a null hypothesis that is actually true, while Type II error occurs when we fail to reject a null hypothesis that is actually false. In other words, Type I error is a false positive, while Type II error is a false negative. The probability of making a Type I error is denoted by alpha (α), while the probability of making a Type II error is denoted by beta (β).

6. What is p-value and how is it used in hypothesis testing?

A p-value is the probability of obtaining a test statistic as extreme as or more extreme than the one observed, assuming that the null hypothesis is true. In hypothesis testing, we compare the p-value to the significance level (alpha) to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than or equal to the significance level, we reject the null hypothesis and conclude that there is evidence for the alternative hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence for the alternative hypothesis.

7. What is the difference between correlation and causation?

Correlation refers to a statistical relationship between two variables, where a change in one variable is associated with a change in the other variable. However, correlation does not imply causation, which means that just because two variables are correlated does not mean that one causes the other. For example, ice cream sales and crime rates may be positively correlated, but that does not mean that ice cream causes crime or that crime causes ice cream sales.

8. What is the difference between a confidence interval and a prediction interval?

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. For example, a 95% confidence interval for the population mean would indicate that if we were to repeatedly sample from the population and compute confidence intervals, 95% of those intervals would contain the true population mean.

A prediction interval, on the other hand, is a range of values that we are fairly certain contains the value of a new observation given the observed data. For example, a 95% prediction interval for a single new observation would mean that we are 95% certain that the new observation falls within the range of the prediction interval. The prediction interval takes into account both the uncertainty in the estimated population parameter and the variability of the individual observations.

9. What is multicollinearity and how can it affect regression models?

Multicollinearity refers to the situation where two or more predictor variables in a regression model are highly correlated with each other. This can cause problems in the regression model because it can be difficult to distinguish the effects of each predictor variable on the response variable. In addition, the coefficients of the predictor variables can become unstable and difficult to interpret. For example, consider a regression model where we are predicting the price of a house based on the square footage and the number of bedrooms. If the square footage and number of bedrooms are highly correlated with each other, it can be difficult to determine the individual effect of each predictor variable on the price of the house.

10. What is the difference between a one-tailed and two-tailed test?

A one-tailed test is a hypothesis test where we are only interested in detecting a change in one direction. For example, we may be interested in testing whether a new drug is better than the existing drug, in which case we would only be interested in detecting an improvement in the response variable. A two-tailed test, on the other hand, is a hypothesis test where we are interested in detecting a change in either direction. For example, we may be interested in testing whether a new diet plan leads to a change in weight, in which case we would be interested in detecting either an increase or decrease in weight. The choice between a one-tailed and two-tailed test should be based on the research question and the direction of the expected effect.

11. What is a hypothesis test and how is it conducted?

A hypothesis test is a statistical method used to determine whether a hypothesis about a population parameter is supported by the sample data. The process typically involves the following steps:

State the null hypothesis and the alternative hypothesis

Choose a significance level (alpha)

Calculate a test statistic based on the sample data

Calculate the p-value

Compare the p-value to the significance level

Draw a conclusion based on the comparison of the p-value and significance level.

For example, suppose we want to test whether the mean weight of apples from a certain orchard is equal to 100 grams. The null hypothesis would be that the mean weight of apples is equal to 100 grams, while the alternative hypothesis would be that the mean weight is different from 100 grams. We would then collect a sample of apples from the orchard and calculate the sample mean weight. We would then use a t-test to calculate the p-value and compare it to the chosen significance level. If the p-value is less than or equal to the significance level, we reject the null hypothesis and conclude that the mean weight of apples is different from 100 grams.

12. What is a sampling distribution and why is it important in statistical inference?

A sampling distribution is the distribution of a statistic (e.g. mean, proportion) calculated from all possible samples of a given size from a population. It is important in statistical inference because it allows us to make probabilistic statements about the population parameter based on sample statistics. Specifically, the sampling distribution provides information about the variability of the statistic and the distribution of the statistic under repeated sampling. For example, the central limit theorem states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough, regardless of the distribution of the population. This allows us to use normal distribution properties to make inferences about the population mean.

13. What is overfitting and how can it be prevented?

Overfitting is a common problem in machine learning where a model is too complex and fits the training data too closely, resulting in poor performance on new, unseen data. Overfitting can be prevented by using regularization techniques, such as L1 or L2 regularization, which add a penalty term to the loss function to discourage overfitting. Other techniques include early stopping, which stops training when the validation error starts to increase, and reducing the complexity of the model by removing unnecessary features

14. What is the difference between descriptive and inferential statistics?

Descriptive statistics are used to summarize and describe the main features of a dataset, such as the mean, median, mode, and standard deviation. Inferential statistics, on the other hand, are used to draw conclusions or make inferences about a larger population based on a sample of data..

15. What is regularization and how does it help with overfitting?

Regularization is a technique used in machine learning to prevent overfitting of a model. Overfitting occurs when a model fits the training data too well, including the noise or random fluctuations, and as a result, it does not generalize well to new data.

Regularization works by adding a penalty term to the cost function of the model, which increases the cost of certain model parameters that cause overfitting. This penalty encourages the model to choose simpler coefficients or features that generalize well to new data.

There are two common types of regularization techniques:

L1 Regularization (Lasso): It adds a penalty term that is proportional to the absolute value of the model parameters. This penalty tends to shrink some parameters to zero, effectively performing feature selection and making the model sparse.

L2 Regularization (Ridge): It adds a penalty term that is proportional to the square of the model parameters. This penalty tends to spread the impact of each feature across all the output variables, making the model less sensitive to changes in a single feature.

By introducing regularization, the model learns to balance the trade-off between fitting the training data and generalizing to new data, resulting in improved model performance. Regularization helps to reduce the variance of the model, which is the difference between the expected value of the model predictions and the true values of the target variable.

Numerical based interview questions

"Essential Numerical Interview Questions for Data Science: Unleashing the Power of Statistics"

Numerical questionsmedium.com

Soon coming more interview questions……..

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