Statistical Significance

Correct Answer: The feedback is 1.75 standard deviations below the mean, the usability may need improvement.

A Z-score provides an indication of how far an individual data point is from the mean, in terms of standard deviations. A Z-score of -1.75 implies that the feedback is 1.75 standard deviations below the mean. This often indicates potential areas for improvement. Contrary to one of the provided answers, Z-scores are indeed used in statistical analysis as they provide a method of comparing data points from different sets, even when the sets are based on different scales. Also, Z-scores don't suggest percentages of data, unlike another option provided here, but rather are a measurement of distance from the mean using standard deviations. The remaining answer choice incorrectly suggests that the feedback is 1.75 standard deviations above the mean, while in reality, a negative Z-score always suggests the value is below the mean.

Correct Answer: The customer satisfaction rate is significantly lower than the population mean.

A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. A negative z-score indicates that the data point is less than the mean and is below the mean data point. A z-score of -2.5 means that the customer satisfaction rating is significantly below the average, hence, 'The customer satisfaction rate is significantly lower than the population mean.' is the correct answer. The statement 'The customer satisfaction rate is significantly higher than the population mean.' is incorrect because a negative z-score means the value is below, not above, the mean. The statement 'The customer satisfaction rate is close to the population mean.' is incorrect because a z-score of -2.5 represents a value far from the mean. Lastly, the statement 'The customer satisfaction rate is equal to the population mean.' is incorrect as well because a z-score of 0 indicates a value equal to the mean, not -2.5.

Correct Answer: The observed value is 2.6 standard deviations above the mean, which indicates a significant difference.

The Z-score in statistics represents the number of standard deviations an element is from the mean. So, a Z-score of 2.6 means that the observed value (in this case, customer complaint data) is 2.6 standard deviations above the mean. This suggests that the number of complaints is significantly higher than average. Hence, the Agile team needs to pay serious attention. The alternative answer stressing on the Z-score being irrelevant cannot be correct as Z-score is a necessary part in data analysis and specially, it becomes quite significant when it is this high. The responses suggesting that the observed value is below the mean or non-significant are incorrect too, when the Z-score is above 2, it can't be non-significant or below the average.