The variance of cereal boxes

BASICS BUSINESS STATISTICS
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Answer
1.1.1) The expected frequencies were evaluated from the past information on percentages of
number of commuters availing transports.
The chi-square values were calculated using the formula
χ2= ( Obs−Exp ) 2
Exp for ‘N-1’
degrees of freedom. Table 1 contains the detailed calculations of Chi-square test in Excel.
Null hypothesis: There is no significant difference between the observed and expected
frequencies of residents availing the three transports.
Alternate hypothesis: There is significant difference between the observed and expected
frequencies of residents availing the three transports.
Significance level: Alpha = 0.05
Test statistic:
χ2= ( Obs−Exp ) 2
Exp =1 . 76+7 .56+ 12. 19=21 .51 where the p-value <
0.05.
Decision: Based on statistical evidences the null hypothesis is rejected at 5% level of
significance.
1.1.2) Conclusion: Information collected by the Mayor significantly differed from the previous
knowledge. Hence, the Mayor might conclude that choice of transport has considerably
changed in recent times.
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Table 1: Chi-square test for goodness of fit for commuters with transport
1.2.1) The claim regarding the variance of weights of cereal boxes has been done using one
sample F-test.
Null hypothesis: The variance of cereal boxes is greater than or equal to 0.003
killograms2.
Alternate hypothesis: The variance of cereal boxes is significantly less than 0.003
killograms2.
Significance level: Alpha = 0.01
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