Question

An experimenter flips a coin 100 times and gets 58 heads. Find the 90% confidence interval for the probability of flipping a head with this coin.
a. [0.483, 0.677]
b. [0.383, 0.627]
c. [0.533, 0.538]
d. [0.483, 0.477]
e. [0.403, 0.677]
f. None of the above

Answer 1

Answer:

The correct option is f.

Step-by-step explanation:

The (1 - α)% confidence interval for the population proportion is:

$CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}$

It is provided that an experimenter flips a coin 100 times and gets 58 heads.

That is the sample proportion of heads is, $\hat p=0.58$.

The critical value of z for 90% confidence level is, z = 1.645.

*Use a z-table.

Compute the 90% confidence interval for the probability of flipping a head with this coin as follows:

$CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}$

     $=0.58\pm 1.645\cdot\sqrt{\frac{0.58\times(1-0.58)}{100}}\\\\=0.58\pm 0.0812\\\\=(0.4988, 0.6612)\\\\\approx (0.499, 0.661)$

Thus, the 90% confidence interval for the probability of flipping a head with this coin is (0.499, 0.661).

The correct option is f.