Question

The standard deviation of the annual precipitations of a region over a period of 100 years was 16 cm. During the last 15 years a standard deviation of annual precipitations was computed as 10 cm. Test the hypothesis that the precipitations in the region have become less variable than in the past, using a significance level of (a) 0.05 and (b) 0.01. Use chi-square distribution.

Answer 1

a)

Ho :   σ =   16
Ha :   σ <   16
      
Level of Significance ,    α =    0.05
sample Std dev ,    s =    10
Sample Size ,   n =    15
      
Chi-Square Statistic   X² = (n-1)s²/σ² =    5.469
      
degree of freedom,   DF=n-1 =    14
      

p-value   =   0.021838807
      
Reject the null hypothesis      

It can be concluded that the precipitations in the region have become less variable than in the past.

b)

Ho :   σ =   16
Ha :   σ <   16
      
Level of Significance ,    α =    0.01
sample Std dev ,    s =    10
Sample Size ,   n =    15
      
Chi-Square Statistic   X² = (n-1)s²/σ² =    5.469
      
degree of freedom,   DF=n-1 =    14
      

p-value   =   0.021838807
      
Do not reject the null hypothesis      

It can not be concluded that the precipitations in the region have become less variable than in the past.

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