Inferential Statistics for Data Science

Select the right answer.

With the help of inferential statistics, we can :

Standard Error is the amount of variation in the _________ data. It is related to Standard Deviation as σ/√n, where, n is the _________ size.

A Sampling Distribution is a probability distribution of a statistic (Mean/Median/Mode) obtained through a large number of samples drawn from a specific population.

A Sampling Distribution behaves much like a normal curve and has some interesting properties like :

Central Limit Theorem states that:

When plotting a sampling distribution of means, the mean of sample means will be equal to the population mean. And the sampling distribution will approach a normal distribution with variance equal to σ/√n where σ is the standard deviation of population and n is the sample size.

Greater the sample size, lower the standard error and greater the accuracy in determining the population mean from the sample mean?

No matter the shape of the population distribution, be it bi-modal, right-skewed, etc. The shape of the Sampling Distribution will remain the same (normal curve)?

For a sampling distribution:

The number of samples has to be sufficient (generally more than 50) to satisfactorily achieve a normal curve distribution. We also have to keep the sample size fixed since any change in sample size will change the shape of the sampling distribution and it will no longer be bell-shaped?

As we increase the sample size, the sampling distribution squeezes from both sides giving a better estimate of the population statistic since it lies somewhere in the middle of the sampling distribution (generally).

The confidence interval is a type of interval estimate from the ___________ distribution which gives a range of values in which the population statistic may lie.

The margin of error is a statistic expressing the amount of random sampling error in the results of a survey.

Margin of Error________ the width of Confidence Interval

Which of the following points are true for confidence intervals?

Hypothesis testing lets us identify ________ statistic to be checked against a _________ statistic or statistic of another sample to study any intervention etc.

Null hypothesis is a type of hypothesis in which we assume that sample observations are not by chance. They are affected by some non-random situation. It is denoted by H1 or Ha.

Alternate Hypothesis is a type of hypothesis in which we assume that the sample observations are purely by chance. It is denoted by H0.

Hypothesis Testing is done on different levels of confidence and makes use of z-score to calculate the probability.

For a 95% Confidence Interval, anything above the z-threshold for 95% would reject the null hypothesis.

Write down the steps to hypothesis testing.

The significance level, also denoted as alpha or α, is the probability of rejecting the null hypothesis when it is ________.

p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.

Low enough p-value is ground for rejecting the null hypothesis. We reject the null hypothesis if the p-value is less than the significance level?

Type-1 error: Type 1 error is the case when we fail to reject the null hypothesis but actually it is false. The probability of having a type-1 error is called beta(β).

Type-2 error: Type 2 error is the case when we reject the null hypothesis but in actual it was true. The probability of having a Type-2 error is called significance level alpha(α).

For Type 1 and Type 2 error:

α= P (Null hypothesis rejected | Null hypothesis is true)

β= P (Null hypothesis accepted | Null hypothesis is false)

Power of test is defined as

P= 1- Type-2 error

= 1 – β

Lesser the type-2 error more the power of the hypothesis test.

For a Z - test:

1. A Z-test is mainly used when the data is normally distributed.
2. We find the Z-statistic of the sample means and calculate the z-score.
3. Z-test is mainly used when the population mean and standard deviation are given.

T-tests are similar to the z-scores, the only difference being that instead of the Population Standard Deviation, we use the Sample Standard Deviation?

Z-tests are statistical calculations that can be used to compare population means to a sample's.

T-tests are calculations used to test a hypothesis, but they are most useful when we need to determine if there is a statistically significant difference between two independent sample groups.

The Degree of Freedom is the number of __________that have the choice of having more than one arbitrary value.

Select the True statement

One-sample t-test compares the mean of _________ data to a known value.

Which of the following points are true for One Sample T- test?

We use a two-sample T-test when we want to evaluate whether the mean of the two independent samples is different or not.

Two-sample T-test is used to:

Points to be noted for two sample T-test are:

1. The groups to be tested should be __________
2. The groups’ distribution should not be highly _________.

A Independent Samples t-test compare the means for ______ different groups?
Samples are __________ of each other?

A Paired sample t-test compares means from the ______ group at different times?
Samples are _________ on each other?

ANOVA is used to determine whether there are any statistically significant differences between the means of ________ independent (unrelated) groups.

A one-way ANOVA has ______ independent variable, while a two-way ANOVA has ______.

Write down the steps to perform ANOVA.

Practical applications of ANOVA in modeling are:

The Chi-Square Test determines whether there is an association between _______ variables (i.e., whether the variables are independent or related).

Goodness of fit: It compares two categorical variables to find whether they are related with each other or not.

Test of Independence: It determines if sample data of categorical variables matches with population or not.

Regression analysis is a form of predictive modelling technique which investigates the relationship between a ___________ (target) and __________ variable (s) (predictor).

The regression sum of squares describes how well a regression model represents the modeled data.
A higher regression sum of squares indicates that the model does not fit the data well?

A residual sum of squares (RSS) is a statistical technique used to measure the amount of_________ in a data set that is not explained by a regression model.

Coefficient of Determination (R-Square): It represents the strength of correlation between two variables?

Correlation Coefficients are used to measure how strong a relationship is between two variables?