A data set lists earthquake depths. The summary statistics are n 400 x = 4.44km,
ID: 3318422 • Letter: A
Question
A data set lists earthquake depths. The summary statistics are n 400 x = 4.44km, s 4.39km Use a 0.05 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean greater than 4.00 km. Assume that a simple random sample has been selected a. Write the claim in symbolic form. b. Whani: i hypothesis and aliemantive hypothesis? c. Using technology, we get a P-value of 0.023. Should we reject the null hypothesis, or fail to reject the null hypothesis? d. Interpret this result.Explanation / Answer
a.
Given that,
population mean(u)=4 km
sample mean, x =4.44 km
standard deviation, s =4.39km
number (n)=400
null, Ho: =4
alternate, H1: >4
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.649
since our test is right-tailed
reject Ho, if to > 1.649
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =4.44-4/(4.39/sqrt(400))
to =2.005
| to | =2.005
critical value
the value of |t | with n-1 = 399 d.f is 1.649
we got |to| =2.005 & | t | =1.649
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 2.0046 ) = 0.02284
hence value of p0.05 > 0.02284,here we reject Ho
ANSWERS
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b.
null, Ho: =4
alternate, H1: >4
test statistic: 2.005
critical value: 1.649
decision: reject Ho
c.
p-value: 0.02284 = 0.023
d.
we have enough evidence to support the claim of seismologist that these earthquakes are from a population with a mean greater than 4km