Question

a television show conducted an experiment to study what happens when buttered toast is dropped on the floor. when 47 buttered slices of toast were dropped, 25 of them landed with the buttered side up and 22 landed with the buttered side down. use a 0.05 significance level to test the claim that toast will land with the buttered side down 50% of the time. use the p - value method. use the normal distribution as an approximation to the binomial distribution. after that, supposing the intent of the experiment was to assess the claim that toast will land with the buttered side down more than 50% of the time, write a conclusion that addresses the intent of the experiment.

let p denote the population proportion of all buttered toast that will land with the buttered side down when dropped. identify the null and alternative hypotheses to test the claim that buttered toast will land with the buttered side down 50% of the time.

$h_0:p$
$h_1:p$
(type integers or decimals. do not round.)

Explanation:

Step1: State the null and alternative hypotheses

The claim is about a proportion. The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_1\) is the claim we are testing.
If the claim is that the proportion \(p\) of toast landing buttered - side down is \(50\%=0.5\), then \(H_0:p = 0.5\).
If we are initially just testing if \(p = 0.5\) (a two - tailed test in the first part, but for the null and alternative setup as per the problem's first request), and then later considering a one - tailed test for \(p>0.5\). But for the null and alternative to test the claim that \(p = 0.5\) (the first part of the problem where we start with the general claim), \(H_1:p
eq0.5\). However, if we consider the second part (the intent of the experiment which is a one - tailed test), but the problem first asks to identify \(H_0\) and \(H_1\) for the claim that \(p = 0.5\) (the initial claim before re - assessing for \(p>0.5\)).

But if we strictly follow the problem's first sub - task (identifying \(H_0\) and \(H_1\) for the claim that toast lands buttered - side down \(50\%\) of the time), the null hypothesis \(H_0\) is \(p = 0.5\) (because the null hypothesis is the statement of no difference or the claim we assume to be true for the purpose of testing) and the alternative hypothesis \(H_1\) is \(p
eq0.5\) (a two - tailed test for the initial hypothesis testing setup as per the first part of the problem's instruction: "test the claim that toast will land with the buttered side down \(50\%\) of the time").

Answer:

\(H_0:p = 0.5\)
\(H_1:p
eq0.5\)