Question

For the hypothesis test H₀​ : μ = 12 against H₁​ : μ < 12 and variance known, calculate the P-value for the following test statistic:

z₀ = −1.75 Round your answer to three decimal places (e.g. 98.765). P-value =

Answer 1

The P-value for the test statistic z₀ = −1.75 in a one-tailed hypothesis test is approximately 0.040, found by looking at the cumulative area to the left in a standard normal distribution.

Step-by-step explanation:

For the hypothesis test H0: μ = 12 against H1: μ < 12 with a known variance, the P-value corresponding to the test statistic z0 = − 1.75 is found by looking for the cumulative area to the left of z = -1.75 in the standard normal distribution. Since this is a one-tailed test to the left, we only consider the area on the left side of z = -1.75.

Using standard normal distribution tables or statistical software, we find that the P-value is approximately 0.040. This P-value represents the likelihood of obtaining a test statistic as extreme as, or more extreme than, the observed value under the assumption that the null hypothesis is true.