Question

A research center claims that 29​% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1000 adults in that​ country, 31​% say that they would travel into space on a commercial flight if they could afford it. At alphaequals0.05​, is there enough evidence to reject the research​ center's claim? Complete parts​ (a) through​ (d) below. ​(a) Identify the claim and state Upper H 0 and Upper H Subscript 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. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not nothing​%. B. nothing​% of adults in the country would travel into space on a commercial flight if they could afford it. C. No more than nothing​% of adults in the country would travel into space on a commercial flight if they could afford it. D. At least nothing​% of adults in the country would travel into space on a commercial flight if they could afford it.

Answer 1

This is a test for population proportion where

the claim is to test if 29​% of adults in a certain country would travel into space on a commercial flight if they could afford it. This is two sided test because we are testing if it is equal to or not and not if greater or less than.

= 29% = 31% n = 1000

Null : The population proportion of adults in a certain country would travel into space on a commercial flight if they could afford it is 29%

Alternative : The population proportion of adults in a certain country would travel into space on a commercial flight if they could afford it is 29%

B. 29​% of adults in the country would travel into space on a commercial flight if they could afford it

This is can be identified from the part of the question 'A research center claims that 29​% of adults'.

= 29% = 31% n = 1000

Test Stat :

Test Stat = 1.3675

p-value = 2P(Z> Test Stat)

= 2 * [1 - P(Z < 1.37)]

= 2 * (1 - 0.9143) ...............using normal tables

p-value = 0.1715

Since p-value > 0.05

We do not reject the claim that 29​% of adults in the country would travel into space on a commercial flight if they could afford it signifiantly.