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Chapter 8: Problem 30

According to a 2017 AAA survey, \(35 \%\) of Americans planned to take a family vacation (a vacation more than 50 miles from home involving two or more immediate family members. Suppose a recent survey of 300 Americans found that 115 planned on taking a family vacation. Carry out the first two steps of a hypothesis test to determine if the proportion of Americans planning a family vacation has changed. Explain how you would fill in the required entries in the figure for # of success, # of observations, and the value in \(\mathrm{H}_{0}\).

Short Answer

Expert verified
Null hypothesis is \(\mathrm{H}_{0}: p = 0.35\), alternative hypothesis is \(\mathrm{H}_{1}: p \neq 0.35\). The # of success is 115 and # of observations is 300.

Step by step solution

01

Set up the Hypothesis

Both null \(\mathrm{H}_{0}\) and alternative hypotheses \(\mathrm{H}_{1}\) must be stated. The null hypothesis is that there is no change, i.e., the proportion of Americans who plan to take a family vacation is still \(35\%\) or \(0.35\). So, \(\mathrm{H}_{0}\): \(p = 0.35\). The alternative hypothesis is that the proportion has changed: \(\mathrm{H}_{1}\): \(p \neq 0.35\).
02

Compute number of success and Total Observations

The number of successes is equivalent to the number of American respondents planning to take a family vacation in the recent survey, which is 115. Hence, # of success = 115. The total number of observations is the total number of respondents in the recent survey, which is 300. Hence, # of observations = 300.

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