Question

a research center claims that 27% 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, 31% say that they would travel into space on a commercial flight if they could afford it. at α = 0.10, is there enough evidence to reject the research centers claim? complete parts (a) through (c) below. (a) identify the claim and state ( h_0 ) and ( h_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.) a. (square%) of adults in the country would travel into space on a commercial flight if they could afford it. b. the percentage adults in the country who would travel into space on a commercial flight if they could afford it is not (square%). c. at least (square%) of adults in the country would travel into space on a commercial flight if they could afford it. d. no more than (square%) of adults in the country would travel into space on a commercial flight if they could afford it.

Explanation:

The research center's claim is about a specific proportion (27%) of adults. In hypothesis testing for proportions, the null hypothesis \(H_0\) is a statement of equality. Here, the claim is that the proportion \(p = 0.27\) (or 27%). The alternative hypothesis \(H_a\) is the complement of the null hypothesis. Since we are just testing if the claim (equality) is false (a two - tailed test in the context of the overall problem, but for part (a) we focus on identifying the claim), the claim is the null hypothesis value.

Answer:

A. 27% of adults in the country would travel into space on a commercial flight if they could afford it.
\(H_0:p = 0.27\) and \(H_a:p
eq0.27\)