g Determine the critical values for these tests of a population standard deviation. (a) A right-tailed test with 16 degrees of freedom at the alphaequals0.01 level of significance (b) A left-tailed test for a sample of size nequals23 at the alphaequals0.1 level of significance (c) A two-tailed test for a sample of size nequals31 at the alphaequals0.1 level of significance
Answers
Answer:
Step-by-step explanation:
We are to find critical values for the test given
a) df =16: Alpha = 0.01 and right tailed
Critical value= 2.583
b) df = 23-1 = 22: alpha = 0.1 and left tailed
critical= -1.717
c)df=31-1 =30: alpha =0.1: two tailed
t =1.697
Critical values can be obtained from critical t tables.
Left tailed will have negative sign and right tailed positive
Final answer:
The critical values for these tests of a population standard deviation can be found via looking up a chi-square distribution table at the specified degrees of freedom and alpha level. For a two-tail test, the alpha value needs to be divided equally in the two tails.
Explanation:
To determine the critical values for these tests of a population standard deviation, we first need to understand the critical values for a chi-squared test. The chi-square test is used when the degrees of freedom and the level of significance (alpha) are known.
(a) A right-tailed test with 16 degrees of freedom at the alpha equals 0.01 level of significance: To find this critical value, we would check a chi-square distribution table at 16 degrees of freedom and alpha equals 0.01. The value we find is the critical value.
(b) A left-tailed test for a sample of size n equals 23 at the alpha equals 0.1 level of significance: Similarly, we would check the chi-square distribution table but this time at 22 degrees of freedom and alpha equals 0.1. Please note that degrees of freedom is calculated as n-1 which gives us 22 in this case.
(c) A two-tailed test for a sample of size n equals 31 at the alpha equals 0.1 level of significance: For a two-tailed test, we distribute the alpha equally in the two tails of the distribution. That means, we lookup chi-square distribution table for 30 degrees of freedom and alpha equals 0.05 to get our critical value.
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Step-by-step explanation:
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Step-by-step explanation:
We are given the following information in the question:
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