A television show conducted an experiment to study what happens when buttered toast is dropped on the floor. Whien 48 buttered stices of toast were dropped, 30 of them landed with the buttered side up and 48 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 lime 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 fand with the buttered side down more than \( 50 \% \) of fie lime, write a condusion that addresses the intent of the experiment. Let p denote the pepulation proportion of ail buttered toast that will land with the buttered side down when dropped identify ihe nuil and atternative hypotheses to test the claim that buttered toast will land with the buttered side down 50\% of the lime. \[ \begin{array}{l} H_{0} \cdot \rho=05 \\ H_{1} \rho \neq 05 \end{array} \] (Type integers or decimals. Do not round) Identify the test statistic. \[ z=\square \] (Round to two decimal places as needed.)
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In this playful toast experiment, let’s dive into some historical context! The longstanding joke about buttered toast typically falling buttered-side down has fascinated people for ages, sparking debates about luck and gravity. According to folklore, this tasty mishap has become a symbol of life's little disappointments, spawning countless memes and anecdotes in popular culture. Now, let's get practical! When conducting experiments like this, a common mistake is ignoring sample size and the assumptions of the binomial distribution when using the normal approximation. In this case, ensure that both np and n(1-p) are greater than 5 for validity. Here, that would be \(48 \times 0.5 = 24\) and \(48 \times 0.5 = 24\), both of which satisfy the conditions! So, let's spread that butter and keep the good vibes rolling!