Question

Find the value of the standard​ score, z, and determine whether to reject the null hypothesis at a 0.01 significance level. Is the alternative hypothesis​ supported? Upper H 0​: muequals21.3 ​seconds, Upper H Subscript a​: mugreater than21.3 ​seconds, nequals100​, x overbarequals21.5 ​seconds, sigmaequals2.0 seconds The value of the standard score is nothing. ​(Round to two decimal places as​ needed.)

Answer 1

Solution:

Given:

Sample Size = n = 100

Sample Mean =

Population Mean =

Population Standard Deviation =

Level of significance =

Hypothesis H0 and Ha are:

Vs

The value of the  standard score:

Now find z critical value:

Since this is right tailed test, find Area

Thus look in z table for Area = 0.9900 or its closest area and find corresponding z critical value.

Area 0.9901 is closest to 0.9900 , thus corresponding z value is 2.3 and 0.03

Thus Z_critical = 2.33

Decision Rule: Reject H0, if z test statistic value > z critical value = 2.33, otherwise we fail to reject H0.

Since z test statistic value = 1.00 < z critical value = 2.33, we fail to reject null hypothesis H0.

Thus the alternative hypothesis​ is not supported.