A high school counselor wants to examine whether the teenage pregnancy rate at her school is different from the rate nationwide. She knows that the rate nationwide is 15 %. She randomly selects 80 female students from her high school. She finds that 9 out of 80 students are either pregnant now or have been pregnant previously

What is your question?

To examine whether the teenage pregnancy rate at the high school is different from the nationwide rate, we can perform a hypothesis test using the data provided. Here are the steps to analyze the results:

Step 1: Define the null and alternative hypotheses:
- Null hypothesis (H0): The teenage pregnancy rate at the high school is equal to the nationwide rate of 15%.
- Alternative hypothesis (HA): The teenage pregnancy rate at the high school is different from the nationwide rate of 15%.

Step 2: Choose the appropriate test statistic:
Since we are comparing a sample proportion to a known population proportion, we will use the z-test.

Step 3: Calculate the test statistic:
The formula for the z-test statistic for proportions is:
z = (p - P) / sqrt[(P * (1 - P)) / n]
where p is the sample proportion, P is the population proportion, and n is the sample size.

In this case, the sample proportion (p) is 9/80 (number of pregnant students divided by the total sample size). The population proportion (P) is 15% or 0.15. The sample size (n) is 80. Plug these values into the formula to calculate the test statistic.

Step 4: Determine the critical value:
The critical value is the value beyond which we reject the null hypothesis. Since we are performing a two-tailed test (HA: p is different from P), we divide the significance level, typically 0.05, by 2 to get the critical values for both tails. Look up the critical values in the standard normal distribution table or use a statistical software/tool.

Step 5: Compare the test statistic and critical value:
If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 6: Interpret the results:
If the null hypothesis is rejected, it implies that the teenage pregnancy rate at the high school is significantly different from the nationwide rate. If the null hypothesis is not rejected, we do not have sufficient evidence to conclude that the teenage pregnancy rate at the high school is different from the nationwide rate.

Perform the calculations, compare the test statistic to the critical value, and make a conclusion based on the results.