# Inferential statistics Python Notes

## Which Python method in statsmodels module is used to perform a hypothesis test for a population proportion?

`proportions_ztest(counts, nobs, value)` is used to perform hypothesis test for a population proportion.

`proportions_ztest` can be imported from the `statsmodels.stats.proportion` library using the following command:

``````from statsmodels.stats.proportion import proportions_ztest
proportions_ztest(counts, nobs, value)```
```

Output

````(1.134556764847714, .53258567853367)`
```

`proportions_ztest` returns the z-score and the two-tailed p-value for the z-test.

## Which Python scipy.stats submodule is used to calculate a confidence interval based on the Student’s t-distribution?

Form the `scipy.stats` submodule, `st.t.intervals` is used to calculate a confidence interval for a variable based on the t-distribution

Example

``````import scipy.stats as st
print(st.t.interval(confindenece_level, degrees_of_freedon, mean, standard_error))
``````

Output

````(425.85746575867464, 432.98768674649464)`
```

`st.t.intervals` returns the confidence interval for the variable based on the t-distribution

## What are the inputs to proportions_ztest method?

`proportions_ztest` can be imported from the `statsmodels.stats.proportion` library using the following command:

``````from statsmodels.stats.proportion import proportions_ztest
proportions_ztest(counts, nobs, value)```
```

The inputs for `proportions_ztest` are `count`, `nobs`, and `value`

## Which Python method from the scipy.stats submodule is used to calculate a confidence interval based on the Normal Distribution?

`st.norm.interval` is the method used from `scipy.stats` submodule to calculate a confidence interval based on the Normal Distribution

Example

``````import scipy.stats as st
print(st.norm.interval(confidence_level, sample_mean, standard_error))``````

Output

````(425.85746575867464, 432.98768674649464)`
```

`st.norm.intervals` returns the confidence interval for the variable based on the a normal distribution.

## What are the inputs to ztest method in Python?

The inputs to `ztest` are `dataframe` and `population_mean`

Example

``````from statsmodels.stats.weightstats import ztest
import pandas as pd
print(ztest(x1 = dataframe,  value = pupulation_mean))``````

`ztest` returns the z-score and the t-tailed p-value

## Which Python module is used to create confidence intervals

The Pythong `scipy` is used to create confidence intervals.

Example

``````import scipy.stats as st
print(st.norm.interval(confidence_level, sample_mean, standard_error))
print(st.t.interval(confindenece_level, degrees_of_freedon, mean, standard_error))``````

`st.norm.intervals` returns the confidence interval for the variable based on the a normal distribution.

`st.t.intervals` returns the confidence interval for the variable based on the t-distribution

## Which Python method is used to perform hypothesis testing for a population mean when the population standard deviation is unknown

`ttest_1samp(dataframe, null hypothesis value)` is used to perform hypothesis testing for a population mean when the population standard deviation is unknown

Example

``````import scipy.stats as st
import pandas as pd
print(st.stats.ttest_1samp(dataframe, hypothesized_population_mean))``````

`ttest_1samp` returns the t-statistic and two-tailed p-value.

## Which Python method is used to perform hypothesis testing for a population mean when the population standard deviation is known

`ztest(dataframe, null_hypothesis_value)` is used to perform hypothesis testing for a population mean when the population standard deviation is known

Example

``````import statsmodels.stats.weightstats import ztest
import pandas as pd
print(ztest(dataframe, hypothesized_population_mean))``````

`ztest` returns the z-score and the two-tailed p-value.

## What are the inputs to ttest_ind method in the scipy module?

`st.ttest_ind(dataFrame['One'], dataFrame['Two'])` takes two DataFrame columns of equal length as input.

`st.ttest_ind(dataFrame['One'], dataFrame['Two'])` returns the calculated t-statistic and the p-value.

## Which Python method is used to perform a hypothesis test for the difference in two population proportions

The `proportions_ztest()` is imported from the `statsmodels.stats.proportion` submodule and is used to perform a hypothesis test for the difference in two population proportions

Example

`````` from statsmodels.stats.proportion import proportions_ztest
proportions_ztest(array_of_samples_meating_condition, array_of_number_of_samples_in_each_group)``````

The function returns the z-score and the two-tailed p-value

## Which Python method is used to perform an unpaired t-test for the difference in two population means?

`st.ttest_ind(x, y)` is used to perform an unpaired t-test for the difference in two population means

Example

``````import scipy.stats as st
import pandas as pd