Question 1. Consider a numerical random variable X. We have a sample of X with

20 observations. We would like to test the following hypothesis test

H₀ : 2

H₁ : < 2

where is the mean of X in the population. Our sample mean is X = 1.9, and the sample standard deviation is s = 0.4. Assuming that the sample size condition is met, compute the test statistic.

Question 2. Using the same information as in Question 1., which of the following statements is true? Note that all the numbers in this question are being rounded to 2 decimal places.

(a)We will reject the Null if the test statistic is greater than 1.73 at = 0.05.

(b)We will reject the Null if the absolute value of the test statistic is greater than 1.73 at = 0.05.

(c)We will reject the Null if the absolute value of the test statistic is greater than 2.09 at = 0.05.

(d)We will reject the Null if the test statistic is smaller than 1.73 at = 0.05.

(e)None of the above.

Question 3. Using the same information as in Question 1., compute the p-value.