To find the P-value for a left-tailed test with a test statistic \( z = -1.83 \), we can refer to a standard normal (Z) distribution table or use a calculator that provides cumulative distribution function (CDF) values for the standard normal distribution.
The P-value in a left-tailed test is given by the area to the left of the test statistic. For \( z = -1.83 \):
- Look up the cumulative probability for \( z = -1.83 \) in the Z-table, or use a calculator. The cumulative probability for \( z = -1.83 \) is approximately \( 0.0336 \).
This means that:
- P-value ≈ 0.0336.
Now, we compare the P-value with the significance level \( \alpha = 0.05 \):
- Since \( 0.0336 < 0.05 \), we reject the null hypothesis.
Thus, the correct answer is:
A) 0.0336; reject the null hypothesis.