A scientist estmates that the mean riftrogen dioxide level in a city is greater than 34 parts per billion. To tast this esimate, you determine the nifrogen dioxide \( \quad 233644194331442835 \quad 2742 \) kevels for 31 rardomily selected days. The results (in parls per billion) are listed \( 193135352834243728 \quad 15 \quad 39 \) to the right Assume that the population standard deviation is 8. At \( \alpha=0.14 \), can 243436351415153221 you surport the scientist's estimate? Complete parts (a) through (e). (a) Whe the clain mathematically and idenitfy \( \mathrm{H}_{0} \) and \( \mathrm{H}_{3} \). Choose from the following. A. \( \mathrm{H}_{3} \) : \( 1<34 \) B. \( H_{0}-\mu=34 \) \( \mathrm{H}_{\mathrm{a}} \cdot \mu \geq 36 \) (claim) \( \mathrm{H}_{\mathrm{a}} \) : \( \mu>34 \) (claim) D. Hio p \( \geq 3 \). (claim) E \( H_{0}: \mu \leq 34 \) \( H_{2}, \underline{y}<34 \) Ha. \( \mu>34 \) (claim) C. \( \mathrm{H}_{0}: \mu \leq 34 \) (claim) \( \mathrm{H}_{\mathrm{a}} \mu>34 \) F. \( \mathrm{H}_{0}-\mu=34 \) (claim) \( \mathrm{H}_{\mathrm{a}}: \mu>34 \) (a) Frid the crical velue and identity the rejection region. \[ z_{2}=108 \text { (Found to two decmal places as needed.) } \] Rajection regun \( z \) \( \square \) 108 (c) Find the standardized test statisic. \( z= \) \( \square \) (Pand io iwd decmal places as needed)

To determine if the scientist's estimate can be supported, we need to perform a hypothesis test. Given: - The mean nitrogen dioxide level in the city is greater than 34 parts per billion. - The population standard deviation is 8. - The sample size is 31. - The results of the 31 randomly selected days are listed. - The significance level is \( \alpha = 0.01 \). (a) Mathematically, the claim is that the mean nitrogen dioxide level in the city is greater than 34 parts per billion. Therefore, the null hypothesis (\( H_0 \)) is that the mean nitrogen dioxide level is less than or equal to 34 parts per billion, and the alternative hypothesis (\( H_a \)) is that the mean nitrogen dioxide level is greater than 34 parts per billion. The correct choice is: B. \( H_0: \mu \leq 34 \) (claim) \( H_a: \mu > 34 \) (claim) (b) To find the critical value, we need to determine the z-score corresponding to the given significance level (\( \alpha = 0.01 \)). The critical value is \( z_{\alpha} = 2.33 \) (found to two decimal places as needed). The rejection region is \( z > 2.33 \). (c) To find the standardized test statistic, we need to calculate the z-score using the sample mean, population standard deviation, and sample size. The sample mean is \( \bar{x} = 233644194331442835 \) (given). The population standard deviation is \( \sigma = 8 \) (given). The sample size is \( n = 31 \) (given). The z-score is calculated as: \[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \] Substitute the values into the formula to find the z-score. The standardized test statistic is approximately \( z \approx 1.626095 \times 10^{17} \) (found to two decimal places as needed).