A research center claims that $$ 28 \% $$ of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1100 adults in that country, $$ 32 \% $$ say that they would travel into space on a commercial flight if they could afford it. At $$ \alpha=0.10 $$, is there enough evidence to reject the research center's claim? Complete parts (a) through (c) below. A) Identify the claim and state $$ \mathrm{H}_{0} $$ and $$ \mathrm{H}_{\mathrm{a}} $$. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) if they could afford it. B. No more than $$ \square $$ \% of adults in the country would travel into space on a commercial flight if they could afford it. C. At least $$ \square \% $$ of adults in the country would travel into space on a commercial flight if they could afford it. D. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not $$ \square \% $$.

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**Part A: Identify the Claim and State $$ \mathrm{H}_{0} $$ and $$ \mathrm{H}_{\mathrm{a}} $$**

**Claim:**
The research center claims that $$ 28\% $$ of adults in the country would travel into space on a commercial flight if they could afford it.

**Hypotheses:**
- **Null Hypothesis ($$ \mathrm{H}_{0} $$)**: $$ p = 0.28 $$  
  *There is no difference from the claimed percentage; $$ 28\% $$ of adults would travel into space.*
  
- **Alternative Hypothesis ($$ \mathrm{H}_{\mathrm{a}} $$)**: $$ p 
eq 0.28 $$  
  *The percentage of adults willing to travel into space differs from $$ 28\% $$.*

**Summary:**
- **Claim:** $$ 28\% $$ of adults would travel into space if they could afford it.
- **$$ \mathrm{H}_{0} $$:** $$ p = 0.28 $$
- **$$ \mathrm{H}_{\mathrm{a}} $$:** $$ p 
eq 0.28 $$

This sets up a two-tailed hypothesis test to determine if the sample data provides sufficient evidence to reject the research center's claim at the $$ \alpha = 0.10 $$ significance level.
**Part A: Identify the Claim and State $$ \mathrm{H}_{0} $$ and $$ \mathrm{H}_{\mathrm{a}} $$** **Claim:** $$ 28\% $$ of adults in the country would travel into space on a commercial flight if they could afford it. **Hypotheses:** - **Null Hypothesis ($$ \mathrm{H}_{0} $$)**: $$ p = 0.28 $$ - **Alternative Hypothesis ($$ \mathrm{H}_{\mathrm{a}} $$)**: $$ p 
eq 0.28 $$ **Summary:** - **Claim:** $$ 28\% $$ of adults would travel into space if they could afford it. - **$$ \mathrm{H}_{0} $$:** $$ p = 0.28 $$ - **$$ \mathrm{H}_{\mathrm{a}} $$:** $$ p 
eq 0.28 $$ This establishes a two-tailed hypothesis test to assess whether the sample data supports rejecting the research center's claim at the $$ \alpha = 0.10 $$ significance level.

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