Let's begin by refreshing our understanding of what a [tex]\( p \)[/tex]-value represents in hypothesis testing.
A [tex]\( p \)[/tex]-value is the probability that the observed data, or something more extreme, would occur if the null hypothesis is true. It helps us determine the strength of the evidence against the null hypothesis.
### Step-by-Step Solution:
1. State the hypotheses:
- Null Hypothesis ( [tex]\( H_0 \)[/tex] ): The population proportion for Country A is equal to the population proportion for Country B.
- Alternative Hypothesis ( [tex]\( H_1 \)[/tex] ): The population proportion for Country A is different from the population proportion for Country B.
2. Calculate the test statistic:
- The test statistic calculated is [tex]\( z = -0.60 \)[/tex].
3. Find the corresponding [tex]\( p \)[/tex]-value using the given [tex]\( z \)[/tex]-table:
- Given the [tex]\( z \)[/tex]-value of [tex]\( -0.60 \)[/tex], we look up the corresponding [tex]\( p \)[/tex]-value from the provided table.
4. Identify the [tex]\( p \)[/tex]-value in the table for [tex]\( z = -0.60 \)[/tex]:
- According to the provided table, for [tex]\( z = -0.60 \)[/tex], the [tex]\( p \)[/tex]-value is [tex]\( 0.274 \)[/tex].
Therefore, the corresponding [tex]\( p \)[/tex]-value for the given test statistic [tex]\( z = -0.60 \)[/tex] is [tex]\( 0.274 \)[/tex].
This [tex]\( p \)[/tex]-value indicates the probability of observing a test statistic as extreme as [tex]\( -0.60 \)[/tex], assuming that the null hypothesis is true.
