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 \\( \alpha = 0.10 \\), is there enough evidence to reject the research centers claim? complete parts (a) through (c) below. on a commercial flight if they could afford it is not \\% c. at least \\% of adults in the country would travel into space on a commercial flight if they could afford it. d. no more than \\% of adults in the country would travel into space on a commercial flight if they could afford it. let \\( p \\) be the population proportion of successes, where a success is an adult in the country who would travel into space on a commercial flight if they could afford it. state \\( h _ { 0 } \\) and \\( h _ { a } \\). select the correct choice below and fill in the answer boxes to complete your choice. (round to two decimal places as needed.) a. \\( h _ { 0 } : p \geq \\) \\( h _ { a } : p < \\) b. \\( h _ { 0 } : p = 0.27 \\) \\( h _ { a } : p \
eq 0.27 \\) c. \\( h _ { 0 } : p \
eq \\) \\( h _ { a } : p = \\) d. \\( h _ { 0 } : p < \\) \\( h _ { a } : p \geq \\) e. \\( h _ { 0 } : p > \\) \\( h _ { a } : p \leq \\) f. \\( h _ { 0 } : p \leq \\) \\( h _ { a } : p > \\) (b) use technology to find the p - value. identify the standardized test statistic. \\( z = \\) (round to two decimal places as needed.)

Explanation:

Step1: Calculate the standard error

The formula for the standard error \(SE=\sqrt{\frac{p(1 - p)}{n}}\), where \(p = 0.27\) (the proportion in the null hypothesis) and \(n=1100\).

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Step2: Calculate the z - statistic

The formula for the z - statistic is \(z=\frac{\hat{p}-p}{SE}\), where \(\hat{p}=0.31\) (the sample proportion) and \(p = 0.27\), \(SE\approx0.0134\)

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Answer:

\(z\approx2.99\)