Asked by Natasha Finkelstein on Jul 19, 2024
Verified
Consider the following hypothesis problem. n = 30
H0: σ2 = 500
S2 = 625
Ha: σ2 ≠ 500
The null hypothesis is to be tested at the 5% level of significance.The critical value(s) from the chi-square distribution table is(are)
A) 42.557.
B) 43.773.
C) 16.047 and 45.722.
D) 16.791 and 46.979.
Null Hypothesis
A hypothesis stating there is no significant difference or effect, or a specified parameter equals a certain value, in the population being studied.
Critical Value(s)
Threshold(s) in hypothesis testing that define the boundary or boundaries for rejecting the null hypothesis.
- Identify key values in chi-square and F distribution tables for the purpose of hypothesis examination.
Verified Answer
AR
alyssa reignJul 21, 2024
Final Answer :
C
Explanation :
Since we are testing the hypothesis about population variance, we need to use the chi-square distribution. The degrees of freedom for this problem is n-1 = 29. Additionally, since it is a two-tailed test, we need to split the 5% level of significance equally into two tails: 2.5% in each tail. Using a chi-square distribution table with 29 degrees of freedom, the critical values for the 2.5% level of significance in each tail are 16.047 and 45.722. Hence, the correct answer is C.
Learning Objectives
- Identify key values in chi-square and F distribution tables for the purpose of hypothesis examination.