A television show conducted an experiment to study what happens when buttered toast is dropped on the floor. When 49 buttered slices of toast were dropped, 31 of them landed with the buttered side up and 18 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 that addresses the intent of the experiment.
(Type integers or decimals. Do not round.)
Identify the test statistic
\[
z=
\]
(Round to two decimal places as needed.)
Identify the P-value.
P-value $=$
(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
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 $H_{0}-p$ down more than $50 \%$ of the time (Type integers or decimals. Do not round.) and $\mathrm{H}_{1}: \mathrm{p} \square \square$. Based on these results, there sufficient evidence to support of the claim that buttered toast will land with the buttered side

Step 1 ：Given that the sample proportion \(\hat{p} = \frac{31}{49}\), the hypothesized population proportion \(p_0 = 0.5\), and the sample size \(n = 49\).

Step 2 ：The test statistic for a proportion is calculated using the formula: \[z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\]

Step 3 ：Substituting the given values into the formula, we get \(z = 1.8571428571428577\).

Step 4 ：Final Answer: The test statistic is \(\boxed{1.86}\).

Step 5 ：The P-value is the probability that a random variable is more extreme than the observed data, assuming the null hypothesis is true. In this case, we are dealing with a two-tailed test, so we need to find the probability that a standard normal random variable is greater than the absolute value of the test statistic.

Step 6 ：Calculating the P-value, we get \(p_{value} = 0.0632908322333452\).

Step 7 ：Final Answer: The P-value is \(\boxed{0.063}\).

Step 8 ：The null hypothesis in this case is that the toast will land with the buttered side down 50% of the time. We reject the null hypothesis if the P-value is less than the significance level. In this case, the significance level is 0.01.

Step 9 ：Since the P-value is greater than the significance level, we do not reject the null hypothesis.

Step 10 ：Final Answer: There is not sufficient evidence to reject the claim that buttered toast will land with the buttered side down $50 \%$ of the time.

Step 11 ：Since we did not reject the null hypothesis, there is not sufficient evidence to support the claim that the toast will land with the buttered side down more than 50% of the time.

Step 12 ：Final Answer: Based on these results, there is not sufficient evidence to support the claim that buttered toast will land with the buttered side down more than $50 \%$ of the time.