Question

a television show conducted an experiment to study what happens when buttered toast is dropped on the floor. when 47 buttered slices of toast were dropped, 25 of them landed with the buttered side up and 22 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. let p denote the population proportion of all buttered toast that will land with the buttered side down when dropped. 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
eq 0.5 ) (type integers or decimals. do not round.) identify the test statistic. ( z=square ) (round to two decimal places as needed)

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}$ is the number of successes (buttered side down) divided by the sample size. Here, the number of buttered - side - down toasts $x = 22$ and the sample size $n=47$. So, $\hat{p}=\frac{x}{n}=\frac{22}{47}\approx0.468$.

Step2: Calculate the test statistic

The formula for the test statistic $z$ in a proportion test is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$, where $p = 0.5$ (the proportion under the null hypothesis).

Substitute the values:

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Answer:

$z\approx - 0.44$