A poll of 92 students found that 48% were in favor of raising tution to pave new parking lots. The standard deviation of this poll is 3%. What would be the standard deviation if the sample size were increased from 92 to 195?

Ah, statistics, the art of making numbers more confusing than they already are. Well, let's see what we can do here.

The standard deviation, you say? Well, if we have a standard deviation of 3% for a sample size of 92, we can try a little formula magic to estimate the standard deviation for a sample size of 195.

The formula we can use is:

\( \text{new standard deviation} = \frac{\text{old standard deviation}}{\sqrt{\text{old sample size}}} \times \sqrt{\text{new sample size}} \)

So, plugging in the numbers, we get:

\( \text{new standard deviation} = \frac{3\%}{\sqrt{92}} \times \sqrt{195} \)

Now, since I'm a clown and not a mathematician, I have no idea what the answer is. But hey, at least I tried to sound smart!

To find the standard deviation when the sample size is increased from 92 to 195, we will use the formula for the standard deviation of a sample.

The formula for the standard deviation of a sample is:
s = sqrt((p * (1 - p)) / n)

Where:
s is the standard deviation
p is the proportion of students in favor of raising tuition to pave new parking lots (48% or 0.48)
n is the sample size (92 in the original case)

Let's calculate the standard deviation using the given information:
s1 = sqrt((0.48 * (1 - 0.48)) / 92)

Now, we need to calculate the new standard deviation when the sample size is increased to 195. We can use the formula again, but this time substituting the new sample size (195) into the equation:
s2 = sqrt((0.48 * (1 - 0.48)) / 195)

Let's calculate the new standard deviation:
s2 = sqrt((0.48 * (1 - 0.48)) / 195)

Therefore, the standard deviation when the sample size is increased from 92 to 195 would be given by s2 = sqrt((0.48 * (1 - 0.48)) / 195).

To determine the standard deviation if the sample size were increased from 92 to 195, we can use a formula that relates the standard deviation to the sample size. This formula is known as the standard error.

The standard error (SE) is calculated using the formula:

SE = (standard deviation) / sqrt(sample size)

Using the information given, we have a standard deviation of 3% and a sample size of 92. Plugging these values into the formula, we have:

SE = 3% / sqrt(92)

To find the standard deviation for a sample size of 195, we can use the SE from the previous calculation and multiply it by sqrt(195/92) to adjust for the change in sample size:

standard deviation (new) = SE * sqrt(new sample size / previous sample size)
= (3% / sqrt(92)) * sqrt(195/92)

Calculating this expression gives us the standard deviation for a sample size of 195.