The problem presented is about conducting a hypothesis test to determine if second-graders from a particular school district perform differently from the nationwide average on a standardized mathematics test. Here's how to approach it:

Step 1: Hypotheses

You need to set up the null hypothesis ($H_0$) and the alternative hypothesis ($H_1$).

• Null Hypothesis ($H_0$): The mean test score of second-graders in the district is equal to the nationwide average, $\mu = 50$.

• Alternative Hypothesis ($H_1$): The mean test score of second-graders in the district is different from the nationwide average, $\mu \neq 50$.

This will be a two-tailed test because the superintendent is concerned whether the mean is either higher or lower than the national average (not specifically one direction).

Step 2: Type of Test

• This is a z-test because the population standard deviation is provided ($\sigma = 18$), and the sample size is large ($n = 55$).

Thus, the hypotheses will be:

• $H_0: \mu = 50$
• $H_1: \mu \neq 50$

The test is a two-tailed z-test.

Would you like more details on how to calculate the test statistic or p-value?

Here are 5 related questions to think about:

1. How do you calculate the test statistic for a z-test?
2. What are the critical z-values for a significance level of $\alpha = 0.05$ in a two-tailed test?
3. How do you interpret a p-value in hypothesis testing?
4. What assumptions need to be met for a z-test to be valid?
5. How would the conclusions differ if the test were one-tailed instead of two-tailed?

Tip:

Always verify if the sample size is large enough for using the z-test when the population standard deviation is known. Generally, a sample size of 30 or more is considered large.