A television show conducted an experiment to study what happens when buttered toast is dropped on the floor. When 54 buttered silices of toast were dropped, 20 of them landed with the buttored side up and 25 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 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 ctaim that toast will tand with the buttored sido down more than of tho time, writo a conctusion that addresses the intent of the experiment.

Let p denote the population proportion of all buttored toast that will land with the buttored side down when dropped. Identify the null and altornative hypothoses to tost the claim that buttored toast will land with the buttered side down of the time.

(Type integers or decimals. Do not round.)
Identify the test statistic.

(Round to two decimal places as needed.)

Ask by Mcfarlane Beck. in the United States

Mar 21,2025

Question

A television show conducted an experiment to study what happens when buttered toast is dropped on the floor. When 54 buttered silices of toast were dropped, 20 of them landed with the buttored side up and 25 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 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 ctaim that toast will tand with the buttored sido down more than of tho time, writo a conctusion that addresses the intent of the experiment.

Let p denote the population proportion of all buttored toast that will land with the buttored side down when dropped. Identify the null and altornative hypothoses to tost the claim that buttored toast will land with the buttered side down of the time.

(Type integers or decimals. Do not round.)
Identify the test statistic.

(Round to two decimal places as needed.)

Ask by Mcfarlane Beck. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

To test the claim that buttered toast will land with the buttered side down $$50\%$$ of the time, we need to identify the null and alternative hypotheses.

Given:
- $$n = 54$$ (total number of buttered slices of toast dropped)
- $$x = 25$$ (number of slices that landed with the buttered side down)
- Significance level $$\alpha = 0.01$$

The null hypothesis ($$H_0$$) is that the proportion of buttered toast that will land with the buttered side down is $$50\%$$, i.e., $$p = 0.5$$.

The alternative hypothesis ($$H_1$$) is that the proportion of buttered toast that will land with the buttered side down is not $$50\%$$, i.e., $$p \neq 0.5$$.

The test statistic for the normal distribution approximation to the binomial distribution is given by:
$$ z = \frac{x - np}{\sqrt{np(1-p)}} $$

Substitute the given values into the formula to calculate the test statistic.
The test statistic $$z$$ is approximately $$-0.544331$$.

Next, we need to calculate the P-value using the test statistic and the significance level $$\alpha = 0.01$$. The P-value represents the probability of observing a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true.

The P-value can be calculated using a standard normal distribution table or a calculator.

After calculating the P-value, we can draw a conclusion based on the intent of the experiment.
Null hypothesis ($$H_0$$): $$p = 0.5$$ Alternative hypothesis ($$H_1$$): $$p \neq 0.5$$ Test statistic ($$z$$): $$-0.54$$

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