A television show conducted an experiment to study what happens when buttered toast is dropped on the floor. When 45 buttered slices of toast were dropped, 25 of them landed with the buttered side up and 20 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. \[ \begin{array}{l} \mathrm{H}_{0}: \mathrm{p}=\mathbf{0 . 5} \\ \mathrm{H}_{1}: \mathrm{p} \neq 0.5 \end{array} \] (Type integers or decimals. Do not round.) Identify the test statistic. \[ z=-.75 \] (Round to two decimal places as needed.) Identify the P-value. $\mathrm{P}$-value $=.453$ (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.
Solution
Step 1 ：The experiment is conducted to test the claim that toast will land with the buttered side down 50% of the time. 45 buttered slices of toast were dropped, 25 of them landed with the buttered side up and 20 landed with the buttered side down.
Step 2 ：The null hypothesis (H0) is that the toast will land with the buttered side down 50% of the time. The alternative hypothesis (H1) is that the toast will not land with the buttered side down 50% of the time.
Step 3 ：The test statistic is calculated to be \(-0.75\) and the P-value is \(0.453\).
Step 4 ：The P-value is greater than the significance level of \(0.05\), so we do not reject the null hypothesis. This means that there is not enough evidence to support the claim that the toast will not land with the buttered side down 50% of the time.
Step 5 ：Final Answer: \(\boxed{\text{There is not enough evidence to reject the null hypothesis. Therefore, there is sufficient evidence to support the claim that buttered toast will land with the buttered side down 50% of the time.}}\)
