Question

A data set lists earthquake depths. The summary statistics are nequals400​, x overbarequals6.89 ​km, sequals4.47 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 6.00. 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?
A.
Upper H 0​: munot equals6.00 km
Upper H 1​: muequals6.00 km
B.
Upper H 0​: muequals6.00 km
Upper H 1​: mugreater than6.00 km
C.
Upper H 0​: muequals6.00 km
Upper H 1​: munot equals6.00 km
D.
Upper H 0​: muequals6.00 km
Upper H 1​: muless than6.00 km
Determine the test statistic.
nothing ​(Round to two decimal places as​ needed.)
Determine the​ P-value.
nothing ​(Round to three decimal places as​ needed.)
State the final conclusion that addresses the original claim.

Answer 1

Solution-:

Given:

Here, is known and n>30 so we use Z test for poppulation mean

Hypothesis:

Upper ​ muequals 6.00 km Vs Upper munot equals6.00 km

i.e. Vs (Two tailed test)

Therefore, Option (C) is correct.

Under the test statistic is ,

(Calculated value)

P-value:

By using MS-Excel command "=1-NORMDIST(3.98,0,1,TRUE())"

  

  

Here, hence, reject  

Conclusion:  We conclude that, a seismologist that these earthquakes are from a population with a mean not equal to 6.