Question

In: Statistics and Probability

Find the value of the standard​ score, z, and determine whether to reject the null hypothesis...

Find the value of the standard​ score, z, and determine whether to reject the null hypothesis at a 0.05 significance level. Is the alternative hypothesis​ supported? Upper H 0 ​: mu equals18.2 ​meters, Upper H Subscript a ​: mu not equals18.2 ​meters, nequals 144​, x overbar equals17.5 ​meters, sigma equals1.4 meters. Two decimal places as needed.

Solutions

Expert Solution

=18.2, =1.4 n= 144, = 17.5, = 0.05

Ho: = 18.2

Ha: 18.2

formula for test statistics is

z = -6.00

test statistics = -6.00

calculate p-Value

p-Value = 2 * P( z < -6.00)

find P( z < -6.00) using normal z table we get

P( z < -6.00) = 0

p-Value = 2 * 0

P-Value = 0

calculate critical value for two tailed test with = 0.05

using normal z table we get

Critical values are= ( -1.96 , 1.96 )

now rule to take decision is

Reject Ho if test statistics lies in rejection region.

from following graph we found that test statistics lies in rejection region

Hence, Null hypothesis is rejected.

Decision:

Therefore, there is enough evidence to support the alternative hypothesis.

orchestra answered 2 years ago
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