Question

a television show conducted an experiment to study what happens when buttered toast is dropped on the floor. when 54 buttered slices of toast were dropped, 35 of them landed with the buttered side up and 19 landed with the buttered side down. use a 0.01 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: Identify the claim

The claim is that toast will land with the buttered side down \(50\%\) of the time. So in symbolic form, \(p = 0.5\). This is the null hypothesis \(H_0\) because it is a statement of equality.

Step2: Form the alternative hypothesis

Since the initial test is just to check if \(p = 0.5\) (a two - tailed test for the first part, but for the hypothesis identification here, the claim is \(p = 0.5\)). However, if we consider the general form for hypothesis testing when the claim is about a proportion. The null hypothesis \(H_0\) is \(p=0.5\) and the alternative hypothesis \(H_1\) is \(p
eq0.5\) (for a two - tailed test which is the standard when the claim is \(p = k\) without prior direction). But if we follow the problem's later part where it first asks to test the claim \(p = 0.5\) (using the P - value method as a two - tailed test for the first hypothesis test in the overall problem, but specifically for hypothesis identification):
The null hypothesis \(H_0:p = 0.5\) (because the claim is \(p = 0.5\) and the null hypothesis is a statement of equality). The alternative hypothesis \(H_1:p
eq0.5\) (since we are testing the claim of equality, the alternative is inequality)

Answer:

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