## Shiny practice items 'Data Science camp', module 2

This app allows you to practice various aspects covered in this module.

Please make sure that you have fully completed the following tasks before continuing with this app:

1. Read the module's learning plan

2. Watch the topic videos and review the lecture notes

3. Work through the SPSS How to guide

The module has the following objectives:

1. Define descriptive and inferential statistics

2. Formulate the difference between the population, sample, and sampling distributions

3. Explain the concept of random sampling error and the central limit theorem

4. Use a confidence interval to learn about a population statistic

5. Calculate probabilities under a normal curve

Please proceed with the practice items by clicking on the links in the top bar of this app. It is not necessary to complete these items in order. We encourage you to work together with a classmate!

There are three types of practice items: theory ('TH'), SPSS ('SP') and multiple choice ('MC').

Thus, you should complete these practice items before joining the lab meeting corresponding to this module.

MBA program
Peter Ebbes

#### Question 1

Use a probability calculator for a standard normal distribution to calculate the probability of observing a Z value in between -2 and 2.

#### Purpose

##### Practice your understanding of the sampling distribution and its implications for learning about a population statistic ($\mu$ or $\pi$). Let's do it!

Click the button to get the samples.

#### Question 1

Describe in your own words what the sampling distribution captures.

#### Question 2

What shape does the sampling distribution have? Is it similar to the shape of the population distribution? Pick a different population distribution in the app menu on the left, and compare its effect on the shape of the sampling distribution.

#### Question 3

Consider again the variable IQ that follows a normal distribution. Use the app settings on the left to change the standard deviation of IQ in the population. Carefully examine the range (x-axis) of the histograms. What do you conclude?

#### Question 4

What effect does the sample size has on the sampling distribution? Go ahead and increase/decrease the sample size of your samples in the app menu on the left.

#### Question 5

Keeping the sample size constant, what effect does changing the number of samples have on the the sampling distribution? Go ahead and increase/decrease the number of samples in the app menu on the left.

#### Purpose

##### Follow the following managerial/research question to further practice your SPSS skills. Let's do it!

In this module's topic you learned about confidence intervals. These are important to learn about population statistics. They also come with very nasty calculations that we do not like to do by hand. At all. Fortunately, SPSS can compute confidence intervals. Practice this using the insurance fraud dataset and the following questions that your manager had asked you the other day (you almost forgot about them!).

#### Question 1

Your manager wants to know about the likelihood that a property was rendered uninhabitable. This would give some insights into how serious and potentially how costly the claims are. She asks you to perform the needed analyses and to report back to her. What do you conclude?

#### Question 2

In addition, the manager wants to have an understanding of how large the claim amount was relative to the coverage on the policy for the claims filed at this company. Do customers tend to have enough coverage? What did you find?

#### Purpose

##### Test your knowledge about the subjects of this module. Let's do it!

1. Which of the following activities is an example of inferential statistics for a quantitative variable?

2. Which of the following symbols should one use to indicate the population proportion?

3. Which of the following statements about inferential statistics is true? Inferential statistics..

4. Joe collects a large random sample of LinkedIn users and observes for each of them how often they logged in to the website in the past 7 days. He finds that the average is 7.8 times and the standard deviation is 9.3. Which of the following expressions is true?

5. To compute a confidence interval for the sample mean, we would use the formula $\bar{X} \pm Z_{c} \times \frac{S}{\sqrt{n}}$. Suppose your manager wants a 98% confidence interval. What value of $Z_{c}$ would you need to use (rounded on 2 digits)?