_The number of transistors reported per a given chip plotted on a log scale in the y axis with the date of introduction on the linear scale x-axis. The blue data points are from a [transistor count table](https://en.wikipedia.org/wiki/Transistor_count#Microprocessors). The red line is an ordinary least squares prediction and the orange line is Moore's law._

The Air Quality Index is calculated with the help of breakpoint ranges as shown in the chart below.

Let's create two arrays to store the AQI ranges and breakpoints so that we can use them later for our calculations.

Hypothesis testing is a form of descriptive statistics used to help us make decisions with the data. From the calculated AQI data, we want to find out if there was a statistically significant difference in average AQI before and after the lockdown was imposed. We will use the left-tailed, [paired Student's t-test](https://en.wikipedia.org/wiki/Student%27s_t-test#Dependent_t-test_for_paired_samples) to compute two test statistics- the [`t statistic`](https://en.wikipedia.org/wiki/T-statistic) and the [`p value`](https://en.wikipedia.org/wiki/P-value). We will then compare these with the corresponding critical values to make a decision.

We will now compare the calculated test statistics with the critical test statistics. The critical `t` value is calculated by looking up the [t-distribution table](https://en.wikipedia.org/wiki/Student%27s_t-distribution#Table_of_selected_values).

From the table above, the critical value is 1.699 for 29 `dof` at a confidence level of 95%. Since we are using the left tailed test, our critical value is -1.699. Clearly, the calculated `t` value is less than the critical value so we can safely reject the null hypothesis.

into the output layer. The output layer creates a prediction which can

then be compared to existing data. The errors are used to calculate the

loss function and update weights in the hidden layer and output

This tutorial was adapted from the work by [Andrew Trask](https://github.com/iamtrask/Grokking-Deep-Learning) (with the author's permission).

into the output layer. The output layer creates a prediction which can

then be compared to existing data. The errors are used to calculate the

loss function and update weights in the hidden layer and output

- _The input layer_:

Let's say that instead of a force acting perpendicularly to the beam, a force was applied to our pole through a wire that was also attached to the ground.

Given the tension in this cord, all you need to solve this problem are the physical locations of these objects.

In response to the forces acting upon the pole, the base generated reaction forces in the x and y directions, as well as a reaction moment.

Let's look at a slightly more complicated model. In this example you will be observing a beam with two cables and an applied force. This time you need to find both the tension in the cords and the reaction forces of the beam. *(Source: [Vector Mechanics for Engineers: Statics](https://www.mheducation.com/highered/product/vector-mechanics-engineers-statics-beer-johnston/M9780077687304.html), Problem 4.106)*

Define distance *a* as 3 meters