Question

Suppose we test the proportions of people who like having a cup of coffee early in the morning for two populations: H₀: p₁= p₂ vs H_a: p₁ < p_2. The sample sizes for these two population are

n₁ = n₂ = 400 and the numbers of people who like coffee are x₁ = 160 and x₂ = 200 respectively.

1) What is the value of the test statistic?

a. -2.8571

b. -2.8427

c. -2.8866

d. -2.828

2) Suppose we take Type I error level to be α = 0.01 in the above population proportion testing. What is your conclusion?

a. Reject H₀

b. Accept H₀

c. Do not know

Answer 1

Solution:

1) What is the value of the test statistic?

Answer: b. -2.8427

2) Suppose we take Type I error level to be α = 0.01 in the above population proportion testing. What is your conclusion?

Answer: a. Reject H₀

Explanation:

1)

The test statistic is:

Where:

Therefore, we have:

  

  

Now using the excel function:

Since the p-value is less than the significance level 0.01, we, therefore, reject the null hypothesis.