The sample standard deviations and sample sizes are given for independent simple

Question

The sample standard deviations and sample sizes are given for independent simple random samples from two populations. Use the two-standard-deviations F-test to conduct the required hypothesis test. Round to three decimal places. s_1 = 0.0782, n_1 = 9, s_2 = 0.2, n_2 = 10; left-tailed test, alpha = 0.05 Test statistic: F = 0.153 Critical value: 0.295. Reject H_0. Test statistic: F = 0.153 Critical value: 0.318. Do not reject H_0. Test statistic: F = 0.153 Critical value: 0.295. Do not reject H_0. Test statistic: F = 0.153 Critical value: 0.310. Reject H_0.

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 / sigma2^2   >=   1  
Ha:    sigma1^2 / sigma2^2   <   1  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical F, as alpha =    0.05   ,      
alpha =    0.05          
df1 = n1 - 1 =    8         
df2 = n2 - 1 =    9          
F (crit) =    0.295148041 = 0.295         
              
Getting the test statistic, as              
s1 =    0.0782          
s2 =    0.2          
              
Thus, F = s1^2/s2^2 =    0.152881 = 0.153

As F < 0.295, we reject Ho.

Hence,

OPTION A: F = 0.153, Critical Value = 0.295, Reject Ho. [ANSWER]          

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