Question

Suppose you ride to school with a friend and often arrive at a particular stop light when it is red. One day she says, “It seems like this light is green only 10% of the time when we get here.” You actually think it is green more often than 10% and want to test this. You keep track of the color of the light (green or not green) the next 20 times you ride together, and find that 4 times out of the 20, the light is green when you arrive. You want to know if your sample provides strong evidence that the true proportion of times the light is green when you arrive is greater than 10%.

1. What is the null hypothesis in words?

2. What is the alternative hypothesis in notation?

Thank you, please if possible explain your reasoning after answering the questions.

Answer 1

1. The null hypothesis is (in words)

The true proportion of times the light is green when you arrive is equal to 0.1

The null hypothesis is (in notation)

2.

the alternative hypothesis in notation

Here p is true proportion.

Since you want to know if your sample provides strong evidence that the true proportion of times the light is green when you arrive is greater than 10% so we use greater than sign in the alternative hypothesis.

If it were to verify "Less than 10%" we would use

If it were to verify " Not equal to 10%" we would use

here sample size is n=20, sample proportion =