Science Practice 2: The student can use mathematics appropriately. Science Practice 5: The student can perform data analysis and evaluation of evidence.

The Irongate Foundry, Ltd., has kept records of on-the- job accidents for many years. Accidents are reported according to which hour of an 8-hour shift they happen. The following table shows their accident report. The union at the foundry wants to know whether accidents are more likely to take place during one hour of the shift rather than another. They are asking you what you think.

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The union at the foundry wants to know whether accidents are more likely to take place during one hour of the shift rather than another. They are asking you what you think.

Chi-square Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis.

χ 2 assumptions Have counts of categorical data & we expect each category to happen at least once. Sample size – to insure that the sample size is large enough we should expect at least five in each category. Observations are mutually exclusive and independent.

Equation O is the observed value E is the expected value The χ 2 test provides a measure of the difference between the observed and expected values (χ 2 value) and the probability that the differences are due to chance alone (the P value)

The chi-square tests the null hypothesis, which states that there is no significant difference between the expected and observed result. H 0 : The observed counts are not statistically different from the expected counts. H a : The observed counts are statistically different from the expected counts.

H 0 : The number of accidents during each shift are equal.

Shift Total Observed Expected (o-e) 2 e

Shift Total Observed Expected (o-e) 2 e Χ 2 =

Three steps to performing the chi- squared test 1.Calculate the chi-squared value 2.Calculate the degrees of freedom 3.Compare the chi-square value with a scale of values given by a standard probability.

2.Calculate the degrees of freedom The degrees of freedom is equal to the number of classes minus one. In the Irongate example there are 7 degrees of freedom because there are 8 shifts. (8-1=7)

Remember that the chi-square is testing the null hypothesis. H 0 : The observed counts are not statistically different from the expected counts. Generally speaking, we can reject the null hypothesis if there is a 95% probability that the difference between the observed and the expected is not due to chance. (p value of 0.05)

Χ 2 = 5.15 df = 7 Critical value = Accept the null hypothesis. There is not a statistically significant difference in the number of accidents that occurred during each shift.

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