Test a claim that the mean amount of lead in the air in U.S, cites is less than 0.087 microgram per cubic meter. it was found that the mean amount of lead in the air for the random sample of 58 US, ottes is OCSS microgram per cubic meter and the standard deviation is 0.068 microgram per cudie meter. At a = 0. 10, can the claim be supported? Complete parts (a) through (e) below. Assume the population is nomally distributed.​(b) Find the critical​ value(s) and identify the rejection​ region(s). The critical​ value(s) is/are t0=______(Use a comma to separate answers as needed. Round to two decimal places as​ needed.) (c) Find the standardized test​ statistic, t. The standardized test statistic is t=​______(Round to two decimal places as​ needed.) (d) Decide whether to reject or fail to reject the null hypothesis. (Reject ,Fail to reject)_____H0 because the standardized test statistic_______(is ,is not), in the rejection region.​

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Test a claim that the mean amount of lead in the air in U.S, cites is less than 0.087 microgram per cubic meter. it was found that the mean amount of lead in the air for the random sample of 58 US, ottes is OCSS microgram per cubic meter and the standard deviation is 0.068 microgram per cudie meter. At a = 0. 10, can the claim be supported? Complete parts (a) through (e) below. Assume the population is nomally distributed. ​(b) Find the critical​ value(s) and identify the rejection​ region(s). The critical​ value(s) is/are t0=______(Use a comma to separate answers as needed. Round to two decimal places as​ needed.) (c) Find the standardized test​ statistic, t. The standardized test statistic is t=​______(Round to two decimal places as​ needed.) (d) Decide whether to reject or fail to reject the null hypothesis. (Reject ,Fail to reject)_____H0 because the standardized test statistic_______(is ,is not), in the rejection region. ​(e) Interpret the decision in the context of the original claim. There______(is, is not), enough evidence at the ___ ​% level of significance to ____(reject, support) the claim that the mean amount of lead in the air in U.S. cities is _______( less than, greater than or equal, equal, not equal, less than or equal, greater than) ____​(Type integers or decimals. Do not​ round.) microgram per cubic meter.
**Hypothesis Testing of Mean Lead Levels in U.S. Cities**

**Problem Statement:**
Test a claim that the mean amount of lead in the air in U.S. cities is less than 0.037 microgram per cubic meter. A random sample of 58 U.S. cities shows a mean of 0.038 microgram per cubic meter with a standard deviation of 0.068 microgram per cubic meter. Perform the test at a significance level of α = 0.10. Assume the population is normally distributed.

**Part (a): Identify the claim and state \( H_0 \) and \( H_a \)**
- Null Hypothesis (\( H_0 \)): \( \mu \geq 0.037 \)
- Alternative Hypothesis (\( H_a \)): \( \mu < 0.037 \)

The claim is the alternative hypothesis.

**Part (b): Find the critical value(s) and identify the rejection region(s)**

- The critical value(s) \( t_0 \) is/are [Box for input].
- Instruction: Round to two decimal places as needed.

*Methodology:*
- The solution involves identifying the critical t-value from the t-distribution table for a one-tailed test at α = 0.10.
- Determine the rejection region using critical value(s).
Transcribed Image Text:**Hypothesis Testing of Mean Lead Levels in U.S. Cities** **Problem Statement:** Test a claim that the mean amount of lead in the air in U.S. cities is less than 0.037 microgram per cubic meter. A random sample of 58 U.S. cities shows a mean of 0.038 microgram per cubic meter with a standard deviation of 0.068 microgram per cubic meter. Perform the test at a significance level of α = 0.10. Assume the population is normally distributed. **Part (a): Identify the claim and state \( H_0 \) and \( H_a \)** - Null Hypothesis (\( H_0 \)): \( \mu \geq 0.037 \) - Alternative Hypothesis (\( H_a \)): \( \mu < 0.037 \) The claim is the alternative hypothesis. **Part (b): Find the critical value(s) and identify the rejection region(s)** - The critical value(s) \( t_0 \) is/are [Box for input]. - Instruction: Round to two decimal places as needed. *Methodology:* - The solution involves identifying the critical t-value from the t-distribution table for a one-tailed test at α = 0.10. - Determine the rejection region using critical value(s).
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