Questions: In a two-tailed test of a single population proportion, sample data has a probability P(z>2.20) ≈ 0.014. At α=0.01, the proper statistical decision to make is: Fail to reject H0 Accept H0 Reject H0

In a two-tailed test of a single population proportion, sample data has a probability P(z>2.20) ≈ 0.014. At α=0.01, the proper statistical decision to make is:
Fail to reject H0
Accept H0
Reject H0

Transcript text: In a two-tailed test of a single population proportion, sample data has a probability $P(z>2.20) \approx 0.014$. At $\alpha=0.01$, the proper statistical decision to make is: Fail to reject $\mathrm{H}_{0}$ Accept $\mathrm{H}_{0}$ Reject $\mathrm{H}_{0}$

Solution

Solution Steps

Step 1: Identify the given information

The problem provides the following information:

The test is a two-tailed test for a single population proportion.
The probability $ P(z > 2.20) \approx 0.014 $.
The significance level $ \alpha = 0.01 $.

Step 2: Determine the p-value for the two-tailed test

Since this is a two-tailed test, the p-value is calculated by doubling the given probability: \[ \text{p-value} = 2 \times P(z > 2.20) = 2 \times 0.014 = 0.028. \]

Step 3: Compare the p-value with the significance level

The significance level $ \alpha = 0.01 $. Compare the p-value (0.028) with $ \alpha $: \[ \text{p-value} = 0.028 > \alpha = 0.01. \]

Step 4: Make the statistical decision

Since the p-value is greater than the significance level, the proper statistical decision is to fail to reject $ \mathrm{H}_{0} $.