Final answer:
To construct a two-sided 98% confidence interval (CI) for the true average college graduation age in State A. We do not have enough evidence to suggest that the average graduation age in State A has increased in 2021.
Step-by-step explanation:
To construct a two-sided 98% confidence interval (CI) for the true average college graduation age in State A, we can use the formula: CI = x ± z * (σ/√n), where x is the sample mean, z is the critical value, σ is the standard deviation, and n is the sample size.
Given that x = 24, σ² = 144, and n = 36, we can calculate the standard deviation, which is σ = √(σ²) = √144 = 12. The critical value can be found using a z-table or calculator, but for a two-sided 98% confidence interval, it is approximately 2.33. Therefore, the confidence interval is 24 ± 2.33 * (12/√36) = 24 ± 7.76 = (16.24, 31.76).
To test whether the average college graduation age in State A has increased in 2021 compared to 2020, we need to examine the confidence interval and the null and alternative hypotheses. The null hypothesis states that the average graduation age in 2021 is the same as in 2020 (μ = 22), while the alternative hypothesis suggests that the average age has increased (μ > 22).
The rejection region depends on the level of significance. In this case, we have a 2% significant level, which corresponds to a critical z-value of 2.05. Since our test statistic z = (24-22)/(12/√36) = 2/(12/√36) ≈ 1, which is less than 2.05, we fail to reject the null hypothesis. Therefore, we do not have enough evidence to suggest that the average graduation age in State A has increased in 2021.