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We first define the null hypothesis and alternative hypothesis as below
H0: variance of nicotine content is equal to 0.644 ( null hypothesis)
H1: variance of nicotine content is not equal to 0.644 ( alternative hypothesis )
we then compute the test statistic where we use the chi-square test = ( ( n -1) / ( 0.644/12) )
= ( ( 20 -1 ) / (0.644) )
= ( ( 19) / ( 0.644) ) = 29.50310559
Taking a 0.05 level of significance, the critical value at ( n - 1) degrees of freedom which is ( 20 - 1) = 19 degrees of freedom is 8.906525 to the left and 32.852327 to the right.
Thus we fail to reject the null hypothesis as the test value ( 29.50310559) falls within the non critical region.
Hence, we may conclude that there is no enough evidence to reject the manufacturers claim that the variance of the nicotine content is 0.644