According to a Pew Research poll conducted in March 2022

Hypothesis Testing

In this case, we are testing the claim that the percentage of U.S. parents who would answer "too much time" is 24%. This is a two-tailed test because we are interested in whether the actual percentage is either less than or greater than 24%.

Let's denote:

• p as the claimed population proportion (0.24 in this case)
• p̂ as the sample proportion (133/556 = 0.2392 in this case)
• n as the sample size (556 in this case)
• α as the significance level (0.01 in this case)

Step 1: State the Hypotheses

The null hypothesis (H0) and the alternative hypothesis (H1) are:

• H0: p = 0.24 (The percentage of parents who would answer "too much time" is 24%)
• H1: p ≠ 0.24 (The percentage of parents who would answer "too much time" is not 24%)

Step 2: Calculate the Test Statistic

The test statistic for a proportion is a z-score (z). It's calculated as:

z = (p̂ - p) / sqrt[ p(1 - p) / n ]

Step 3: Determine the Critical Value and Rejection Regions

For a two-tailed test with α = 0.01, the critical value for z is approximately ±2.58. This means the rejection regions are z < -2.58 and z > 2.58.

Step 4: Make a Decision

If the calculated z-score falls within the rejection region, we reject the null hypothesis. If it does not, we fail to reject the null hypothesis.

Step 5: Interpret the Result

If we reject the null hypothesis, it suggests that the percentage of U.S. parents who would answer "too much time" is not 24%. If we fail to reject the null hypothesis, it suggests that the data does not provide strong evidence against the claim that the percentage is 24%.

Remember, failing to reject the null hypothesis does not prove it is true. It simply suggests that the data does not provide strong evidence against it.