# Consistency of sample with value for Parametric Distribution Analysis (Right Censoring)

## Consistency of sample with value – test for scale equal to 0.5

You can test whether distribution parameters are equal to a specified value, such as parameters from an historical distribution.

A chi-square test determines whether the distribution parameter is significantly different from the specified value. Compare the p-value with your pre-determined α-value.
• If the p-value is less than the α-value, then you can conclude that the distribution parameter is significantly different from the specified value.
• If the p-value is greater than the α-value, then you cannot conclude that the distribution parameter is significantly different from the specified value.

### Interpretation

For the engine windings data, the test is whether the scale parameter of the lognormal distribution for the engine windings performing at 80° C is significantly different from 0.5. According to historical data, the scale parameter is usually 0.5.

Because the p-value of 0.823 is greater than an α-value of 0.05, the engineer does not have sufficient evidence to conclude that the scale parameter is significantly different from 0.5. Thus, the engineer assumes that the scale parameter for the current data does not differ from the historical scale value.

## Consistency of sample with value – Bonferroni confidence interval

Minitab also provides a Bonferroni confidence interval, which is associated with a chi-square test, to provide an interval of reasonable values for the parameter.

• When the chi-square test is significant (when you reject it), the corresponding confidence interval will not contain the specified value.
• When the chi-square test is not significant (when you fail to reject it), then typically the corresponding confidence interval will contain the value specified for the test.

### Interpretation

For the engine windings data, reasonable values for the lognormal scale parameter for the windings that are tested at 80° C are between 0.3808 and 0.6208. Notice that the interval includes 0.5 because there was not sufficient evidence to reject the null hypothesis that scale = 0.5.

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