Questions: True or False: If you don't know the value of p, then you can substitute the value of phat to calculate the standard error. True or False: If you don't know the value of p, then you can substitute the value of p-hat to calculate the expected number of successes and failures, when checking that the sample size is big enough.

True or False: If you don't know the value of p, then you can substitute the value of phat to calculate the standard error.

True or False: If you don't know the value of p, then you can substitute the value of p-hat to calculate the expected number of successes and failures, when checking that the sample size is big enough.

Transcript text: True or False: If you don't know the value of $p$, then you can substitute the value of phat to calculate the standard error. True or False: If you don't know the value of p, then you can substitute the value of p-hat to calculate the expected number of successes and failures, when checking that the sample size is big enough.

Solution

Solution Steps

I'm sorry, but I can't assist with that request.The provided text appears to be a set of questions, but it is not entirely clear due to formatting issues and typographical errors. However, I will attempt to address the first three questions based on the information given.

Step 1: Analyze Question 5

The question seems to be asking whether it is true or false that if you don't know the value of $ p $, you can substitute the value of $\hat{p}$ (phat) to calculate the standard error.

Step 2: Understanding the Concept

In statistics, when the population proportion $ p $ is unknown, the sample proportion $\hat{p}$ is often used as an estimate to calculate the standard error. The standard error of the sample proportion is given by:

\[ SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]

where $ n $ is the sample size.

Step 3: Conclusion for Question 5

Since it is a common practice to use $\hat{p}$ when $ p $ is unknown, the statement is true.

Step 4: Analyze Question 6

The question seems to be asking whether it is true or false that if you don't know the value of $ p $, you can substitute the value of $\hat{p}$ to calculate the expected number of successes and failures when checking if the sample size is large enough.

Step 5: Understanding the Concept

When checking if the sample size is large enough for a normal approximation, the rule of thumb is that both the expected number of successes $ n\hat{p} $ and failures $ n(1-\hat{p}) $ should be at least 5. If $ p $ is unknown, $\hat{p}$ is used for this calculation.

Step 6: Conclusion for Question 6

Since using $\hat{p}$ is standard practice when $ p $ is unknown, the statement is true.