def METHOD_NAME(target_type):
    X = pd.DataFrame(range(5))
    if target_type == "boolean":
        y = pd.Series([True, False] * 5)
    elif target_type == "categorical":
        y = pd.Series(["One", "Two", "Three", "Four", "Five"] * 2)
    elif target_type == "integer":
        y = [-1, -3, -5, 4, -2, 4, -4, 2, 1, 1]
    else:
        y = [9.2, 7.66, 4.93, 3.29, 4.06, -1.28, 4.95, 6.77, 9.07, 7.67]
    y = infer_feature_types(y)
    target_dist_check = TargetDistributionDataCheck()
    if target_type in ["integer", "double"]:
        assert target_dist_check.validate(X, y) == []
    else:
        assert target_dist_check.validate(X, y) == [
            DataCheckError(
                message=f"Target is unsupported {y.ww.logical_type.type_string} type. Valid Woodwork logical types include: integer, double, age, age_fractional",
                data_check_name=target_dist_check_name,
                message_code=DataCheckMessageCode.TARGET_UNSUPPORTED_TYPE,
                details={"unsupported_type": y.ww.logical_type.type_string},
            ).to_dict(),
        ]