Question

a television show conducted an experiment to study what happens when buttered toast is dropped on the floor. when 52 buttered slices of toast were dropped, 28 of them landed with the buttered side up and 24 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.

z = - 0.56
(round to two decimal places as needed.)

identify the p - value.

p - value = 0.575
(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.

the null hypothesis. there sufficient evidence to the claim that buttered toast will land with the buttered side down 50% of the time.

Explanation:

Step1: Compare P - value and significance level

Given significance level \(\alpha = 0.05\) and \(P - value=0.575\).
Since \(P - value(0.575)> \alpha(0.05)\).

Step2: Conclusion about null hypothesis

When \(P - value>\alpha\), we fail to reject the null hypothesis.
The null hypothesis \(H_0:p = 0.5\) (where \(p\) is the proportion of buttered toast landing buttered - side down).
The original claim is \(H_0:p = 0.5\).

Answer:

Fail to reject the null hypothesis. There is not sufficient evidence to reject the claim that buttered toast will land with the buttered side down \(50\%\) of the time.

For the second claim (toast will land with the buttered side down more than \(50\%\) of the time, i.e., \(H_1:p>0.5\)):
Since we failed to reject \(H_0:p = 0.5\) (in the two - tailed test which is more conservative than a one - tailed test for \(p = 0.5\) vs \(p>0.5\) in terms of not rejecting the null when \(P - value\) is large), there is not sufficient evidence to support the claim that toast will land with the buttered side down more than \(50\%\) of the time.