Question

1. for each test of hypothesis, sketch the normal distribution, shade the area of ha, and find the p - value.

a) h0: μ = 100 ha: μ < 100
if n = 32 and z = - 1.78, find the p - value of z = - 1.78

Explanation:

Step1: Identify the type of test

This is a one - sided (left - tailed) hypothesis test since $H_a:\mu<100$.

Step2: Use the standard normal distribution table

The p - value for a left - tailed test with a z - score of $z=-1.78$ is the area to the left of $z = - 1.78$ under the standard normal curve. Looking up the value in the standard normal distribution table (or using a calculator with a normal distribution function), the area to the left of $z=-1.78$ is $0.0375$.

Answer:

The p - value is $0.0375$.