Question

A data set lists earthquake depths. The summary statistics are nequals500​, x overbarequals4.76 ​km, sequals4.33 km. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 4.00. Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

What are the null and alternative​ hypotheses?

Answer 1

From given information,

Population Mean μ = 4

Standard deviation s = 4.33

Sample size n= 500

Sample mean xbar = 4.76

Here sample is large n = 500 > 30. So, we are using one sample Z test.

Here we want to test the claim that a seismologist that these earthquake are from a population with mean equals 4 km.

1. Null Hypothesis H₀ : μ = 4 km

Alternative Hypothesis is H_a : μ ≠ 4 km

           Here level of significance α=0.01

2. Test statistic:   Z score = Xbar – μσn

Z = (4.76 - 4) / (4.33/sqrt(500))= 3.925

Z = 3.925

3. P value = 2*(z > 3.925) = 2*( 1- (=NORM.S.DIST(3.925,TRUE))) = 0.0001

Since P value = 0.0001 < 0.01, so we reject null hypothesis at 0.01 level of significance.

4. At the 1% significance level, there is enough evidence to claim that a seismologist that these earthquake are from a population with mean not equal to 4 km.