Question: in the northern hemisphere the day is always shorter at higher latitudes than at lower latitudes

Answer: No, Given that Earth's own axis of rotation is tilted about 23.5° to the line perpendicular to its orbital plane, called the ecliptic, the length of daytime varies with the seasons on the planet's surface, depending on the observer's latitude. Areas tilted toward the Sun are experiencing summer. Their tilt toward the Sun leads to more than half of the day seeing daylight and warmer temperatures, due to the higher directness of solar rays, the longer period of daytime itself, and less absorption of sunlight in the atmosphere. While increased daylight can have some effect on the higher temperatures in the summer, most of temperature rise results from the directness of the Sun, not the increased daylight. The high angles (around the zenith) of the Sun causes the tropics to be warm, while low angles (barely above the horizon) causes the polar regions to be cold. The slight effect of daylight hours on average seasonal temperature can be seen with the poles and tropical regions. The poles are still cold during their respective summers, despite seeing 24 hours of daylight for six months, while the Equator remains warm throughout the year, with only 12 hours of daylight per day.