IMathAS-libretexts

Hint 1 Hint 2 Hint 3

If we increase the sample size to 100, the standard deviation decreases to approximately 0.05, as shown.

A normal curve which is also centered at about 0.64, but is much narrower with a lower standard deviation than in the previous image

How is the test statistic affected if p-hat = 0.74 as before? Choose the correct statement.

The test statistics is still about 1 since the distance between p-hat and p_o is the same as before.
The test statistics increases to about 2 since p-hat = 0.74 is about 2 standard deviations above p_o = 0.64.
The test statistic decreases to about 0.5 since the standard deviation decreases to half of its previous size.

For which sample size does p-hat = 0.74 provide stronger evidence against a null hypothesis of p = 0.60?

n = 25

n = 100

n = 500

In general, the further the test statistic is from 0, the the evidence against the null hypothesis.