The chance of making a Type II statistical error increases if the "true" population mean is closer to the hypothesized population mean, all other factors held constant.

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A Type II error occurs when a false null hypothesis is not rejected. If the true population mean is closer to the hypothesized mean, it becomes harder to detect a difference, thus increasing the chance of failing to reject a false null hypothesis (Type II error).

The Chance of Making a Type II Statistical Error Increases