A popular theme park claims that their weekly attendance is around $100,000$. You believe that the weekly attendance is different than this claimed value, so you gather sample data. Write the null and alternative hypotheses.

• A. $H_0:$ $\mu =100,000$$H_{a}:$ $\mu >100,000$
• B. $H_0:$ $\mu =100,000$$H_{a}:$ $\mu \ne 100,000$
• C. $H_0:$ $\mu=100,000$$H_{a}:$ $\mu$ < $100,000$
• D. $H_0:$ $\mu\ne100,000$$H_{a}:$ $\mu=100,000$

Answer: (B)

Verified step by step guidance

1. Understand the context: The theme park claims their weekly attendance is 100,000. You suspect it is different, which suggests a two-tailed test.
2. Define the null hypothesis (H0): The null hypothesis represents the status quo or the claim being tested. In this case, H0: μ = 100,000, where μ is the population mean of weekly attendance.
3. Define the alternative hypothesis (Ha): The alternative hypothesis represents the claim you are testing against the null hypothesis. Since you believe the attendance is different, Ha: μ ≠ 100,000.
4. Recognize the type of test: Since the alternative hypothesis is not equal (≠), this is a two-tailed test, which checks for any significant difference from the claimed value.
5. Consider the implications: If the sample data provides enough evidence to reject the null hypothesis, it suggests the true mean attendance is significantly different from 100,000.