Question

A scientist claims that 7% of viruses are airborne.

If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 418 viruses would be greater than 6%? Round your answer to four decimal places.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.07

H_a : p > 0.07

n = 418

= 0.06

P₀ = 0.07

1 - P₀ = 1 - 0.07 = 0.93

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.06 - 0.07 / [(0.07 * 0.93) / 418]

= -0.80

Test statistic = -0.80

This is the right tailed test .

P(z > -0.80) = 1 - P(z < -0.80) = 1 - 0.2119

Probability = 0.7881