Question

A data set lists earthquake depths. The summary statistics are nequals500​, x overbarequals5.43 ​km, sequals4.76 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 5.00. 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.

Answer 1

I ) Null and alternative hypotheses

Ho : = 5.00

H1 : 5.00

II) test statistic t = ( xbar - )/(s/√n)

t = ( 5.43 - 5.00)/(4.76/√500)

Test statistic t = 2.02

III) p-value for t = 2.02 and d.f = n -1 = 499

p-value = 2* P( t > 2.02) d.f = 499

p-value = 0.0439

IV) Decision rule : Reject the null hypothesis if p-value < a otherwise we fail to reject the null hypothesis

Our p-value = 0.0439 < 0.05

Conclusion : Reject the null hypothesis Ho , There is no sufficient evidence to support the claim that seismologist that these earthquakes are from a population with a mean equal to 5.00