Question

Suppose we use the following code to generate a sample of height measurements in cm :

set. seed(θ)
x=rnorm(50,175,10)
​
We want to check that the average population height is more than 170 cm. At which level we can reject the null hypothesis? (Select all that apply)
1. 0.05
2. 0.005
3. 0.01
4. 0.1

Answer 1

The null hypothesis can be rejected at a significance level of 0.05 and 0.01, but not at 0.1.

Step-by-step explanation:

When conducting a hypothesis test to check if the average population height is more than 170 cm, we calculate the p-value. The p-value represents the probability of obtaining a sample mean as extreme as or more extreme than the observed sample mean, assuming the null hypothesis is true. The p-value is compared to the significance level (alpha) to decide if the null hypothesis should be rejected or not. Given the choices, we can reject the null hypothesis at a significance level of 0.05 (option 2) and 0.01 (option 1), but not at a significance level of 0.01 (option 4) or 0.1 (option 3).