C3_W4_Quiz.md

1. In statistical hypothesis testing, which of the following statements correctly defines Type Ⅰ and Type Ⅱ errors?

• Type Ⅰ errror occurs when we reject a null hypothesis that is true, while Type Ⅱ error occurs when we do not reject a null hypothesis that is false.
• Type Ⅰ errror occurs when we do not reject a null hypothesis that is true, while Type Ⅱ error occurs when we reject a null hypothesis that is false.
• Type Ⅰ errror occurs when we reject a null hypothesis that is false, while Type Ⅱ error occurs when we do not reject a null hypothesis that is true.
• Type Ⅰ errror occurs when we do not reject a null hypothesis that is false, while Type Ⅱ error occurs when we reject a null hypothesis that is true.

2. About the t-distribution, select all that apply.

• The t-distribution has a mean of 0 and a standard deviation of 1.
• The t-distribution has thicker tails compared to the standard normal distribution.
• The t-distribution gets closer to the Standard Normal distribution when the degrees of freedom increase.
• The t-distribution can be used for testing population means.

3. When conducting a hypothesis test, what are the general steps to decide whether to reject the null hypothesis ($H_{0}$) or not? Seelct the correct sequence of steps. Suppose you have already defined the null hypothesis and the alternative hypothesis.

• Calculate the test statistic, determine the significance level, calculate the p-value, compare the p-value with the significance level, and make a decision.
• Calculate the p-value, set the significance level, compare the p-value with the significance level, and make a decision.
• Set the significance level, calculate the test statistic, calculate the p-value, compare it with the significance level, and make a decision.

4. When defining the null hypothesis ($H_{0}$) and alternative hypothesis ($H_{1}$) in a hypothesis test comparing the average sales before ($\mu_{before}$) and after ($\mu_{after}$) implementing a marketing campaign, which of the following options provides a suitable definition for H0 and H1 for testing if the campaign has increased the sales (select all that apply)?

• $H_{0} \colon \mu_{before} \ge \mu_{after}. H_{1} \colon \mu_{before} \lt \mu_{after}.$
• $H_{0} \colon \mu_{before} = \mu_{after}. H_{1} \colon \mu_{before} \le \mu_{after}.$
• $H_{0} \colon \mu_{before} = \mu_{after}. H_{1} \colon \mu_{before} \ge \mu_{after}.$
• $H_{0} \colon \mu_{before} = \mu_{after}. H_{1} \colon \mu_{before} \lt \mu_{after}.$

5. Suppose you are conducting a hypothesis test to determine whether a new teaching method improves student performance.

The null hypothesis ($H_{0}$) states that the teaching method has no effect, while the alternative hypothesis ($H_{1}$) suggests that the teaching method leads to higher student performance. You collect data from a sample of 50 students and calculate a test statistic of 1.98. The critical value at a significance level of 0.05 is 1.96. Should you reject the null hypothesis?

• No
• Yes

6. A company claims that their new energy drink decreases reaction times. To investigate this claim, a researcher conducts a hypothesis test using a sample of 40 participants. The average reaction time in the sample is 0.95 seconds, with a standard deviation of 0.12 seconds. The company states that the average reaction time without their energy drink is 1.05 seconds. The researcher wants to determine whether there is sufficient evidence to support the company's claim. Assuming a significance level of 0.05, what is the test statistic for this hypothesis test?

• $5.27$
• $-5.27$
• $2.73$
• $-2.73$

7. In the question above, to find p-values for different levels of significance, which distribution would you have to work with?

• Standard Normal Distribution.
• t-Student Distribution with 40 degrees of freedom.
• Normal Distribution with $\mu = 0.95$ and $\sigma = 0.12$.
• t-Student Distribution with 39 degrees of freedom.