Question

among a simple random sample of 331 american adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school. what is the test statistic? what is the p-value assiocated with the hypothesis test?

Answer 1

To calculate the test statistic and p-value, we need to know the sample size, the proportion of adults who cannot afford school, and the expected proportion of adults who cannot afford school in the population. Using the given values, we calculate the test statistic as -6.288 and the p-value as approximately 0.000000001.

Step-by-step explanation:

In order to determine the test statistic and p-value for a hypothesis test, we need to know the sample size, the proportion of adults who cannot afford school, and the expected proportion of adults who cannot afford school in the population.

From the given information, we can calculate the test statistic and p-value as follows:

1. Sample size (n) = 331
2. Proportion of adults who cannot afford school (p) = 48% = 0.48
3. Expected proportion of adults who cannot afford school in the population (p_0) = Proportion of high school graduates who enroll in higher education = 66% = 0.66
4. Test statistic (z) = (p - p_0) / sqrt(p_0 * (1 - p_0) / n)
5. P-value = P(Z > |z|)

Using the given values, we can calculate the test statistic:

z = (0.48 - 0.66) / sqrt(0.66 * (1 - 0.66) / 331) = -6.288

Next, we can calculate the p-value:

P(Z > |-6.288|) = 2 * P(Z < -6.288) ≈ 0.000000001

Therefore, the test statistic is -6.288 and the p-value is approximately 0.000000001.