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. 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 = 0.5 ) ( h_1:p
eq0.5 ) (type integers or decimals. do not round.) identify the test statistic. ( z=-2.18 ) (round to two decimal places as needed.) identify the p - value. ( p - value=square ) (round to three decimal places as needed.)

Explanation:

Step1: Determine the type of test

Since \(H_1: p
eq0.5\), this is a two - tailed test.

Step2: Calculate the P - value

For a two - tailed \(z\) - test, the P - value is \(2\times(1 - \Phi(|z|))\), where \(\Phi\) is the cumulative distribution function of the standard normal distribution. Given \(z=- 2.18\), then \(|z| = 2.18\).
Using a standard normal table or a calculator with a normal distribution function (e.g., in Excel: \(=2(1 - NORM.S.DIST(2.18,TRUE))\) or in R: \(2(1 - pnorm(2.18))\)), we find that \(1-\Phi(2.18)\) is the area to the right of \(z = 2.18\) under the standard normal curve.
\(\Phi(2.18)\approx0.9854\), so \(1-\Phi(2.18)=1 - 0.9854=0.0146\). Then \(P - value=2\times0.0146 = 0.0292\approx0.029\)

Answer:

\(P - value = 0.029\)