1.We are interested to study a sensor system and we know that the sensor noise is distributed normally and has a mean of 4.65 and a standard deviation of 0.39 . There is a new sensor which we want to see how it works sowe take 10 measurements and the results are: {4.55, 5.35, 5.3, 4.6, 4.9, 5.5, 4.2, 5.1, 4.1, 4}. Can you show that the sensors generate different data and that the new sensor is more reliable (i.e. has noise with a lower variance)?

Include your calculations and the significance scores.

2. In order to evaluate the runtime performance of an algorithm, we measured it's run time performance on 15 samples and the results are: {17, 16.3, 18.2, 17.9, 16, 16.5, 18.9, 19.9, 18, 18.3, 18.1, 15.7, 17.6, 17.7, 17.1}. The state-of-the-artalgorithm that has an average runtime performance of 17 and a standard deviation of 5.82 . Is there any difference between the first algorithms and the state-of-the-artalgorithm?

Evaluate the significance of the hypothesis, explain and list yourcalculations, test choices, and conclusion drawn.

3. In order to develop a new approach to solve a problem, a student develops a new approach ( Method 1) and the result she gets are: {12, 4, 6, 7, 12, 4, 7, 4, 15, 10, 8, 10, 9, 5, 9}. Method 2 which is the current state-of-the-art approach, has average performance of7 and a standard deviation of 3 . The student compares the result and discovers that it seems that method 1 outperforms method 2 and she wants to prove it using significance testing with a two-tailed 1% significance threshold.

Evaluate the results in terms of the hypothesis that method 1 has a higher performance than method 2. List all the steps (and formulas) involved in the test and what the result implies for the significance of the hypothesis.

4. A researcher wants to do a research on people's body height (in meter) in a specific city so he measures the height of 30 random persons and the results are: {1.9, 1.83, 1.8, 1.7, 1.75, 1.83, 1.6, 1.65, 1.5, 1.42, 1.82, 1.87, 1.53, 1.65, 1.99, 1.78, 1.69, 1.52, 1.62, 1.63, 1.75, 1.8, 1.72, 1.6, 1.82, 1.62, 1.87, 1.75, 1.82, 1.52}. Suppose that from previous studies which has been done 50 years ago, the average height of personswas determined to be 1.73 and standard deviation is 0.2 in this city.

Can this data be used to show that the average height of individuals in this city has changed in the last 50 years(The acceptable threshold for significance is 5%)?(Show your calculations).