Question

television show conducted an experiment to study what happens when buttered toast is dropped on the floor. when 4 buttered slices of toast were dropped, 35 of them landed with the buttered side up and 19 landed with the buttered de down. use a 0.01 significance level to test the claim that toast will land with the buttered side down 50% of the me. use the p - value method. use the normal distribution as an approximation to the binomial distribution. after that, upposing the intent of the experiment was to assess the claim that toast will land with the buttered side down more han 50% of the time, write a conclusion that addresses the intent of the experiment.
p - value = 0.029
(round to three decimal places as needed.)
state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.
fail to reject the null hypothesis. there is not sufficient evidence to warrant rejection of the claim that buttered toast will land with the buttered side down 50% of the time.
write a conclusion that addresses the test that the toast will land with the buttered side down more than 50% of the time.
the intent of the experiment was to test ( h_0:p ) and ( h_1:p ). based on these results, there sufficient evidence to support of the claim that buttered toast will land with the buttered side down more than 50% of the time.
(type integers or decimals. do not round.)

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is a statement of no effect or no difference. Here, the claim that toast lands with the buttered - side down \(50\%\) of the time translates to \(H_0:p = 0.5\). The alternative hypothesis \(H_1\) for the claim that toast lands with the buttered - side down more than \(50\%\) of the time is \(H_1:p>0.5\).

Since the P - value (\(0.029\)) is compared to the significance level. For a one - tailed test (as in \(H_1:p > 0.5\)) with a significance level of \(0.01\), we check if \(P-\text{value}<\alpha\). Here, \(0.029>0.01\).

Answer:

The intent of the experiment was to test \(H_0:p = 0.5\) and \(H_1:p>0.5\). Based on these results, there is not sufficient evidence to support of the claim that buttered toast will land with the buttered side down more than \(50\%\) of the time.