152k views
0 votes
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 =

User Orjanto
by
8.3k points

1 Answer

5 votes

Final answer:

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.

User Recvec
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.