Null and alternative hypotheses

A null hypothesis states that the independent variable (temperature) has no effect on the dependent variable (leakage): any differences are due to chance.

• Correct: The heating temperature has no effect on how much red color leaks from beet cubes.: Correct: no effect.
• Heating beet cubes to higher temperatures increases how much red color leaks out.: This is an alternative hypothesis with a direction.
• Beet cubes heated to 80 °C will turn the water redder than cubes heated to 20 °C.: This is a prediction for two specific groups.
• Heat damages the membranes of beet cells, which lets the red substance escape into the water.: This is a proposed explanation of the effect, not a null hypothesis.

The values overlap almost completely (0.05-0.11 and 0.06-0.12), and the 0.01 gap in means is far smaller than the 0.06 range within each group, so chance could easily produce it.

• Correct: Fail to reject it: the means differ by 0.01, much less than the spread among cubes in either group.: Correct: the difference is no bigger than chance variation.
• Reject it: the 40 °C mean is higher than the 20 °C mean, so heating to 40 °C increased the leakage.: Any two means differ a little; a difference must be larger than the variation within groups to count.
• Accept it: the data prove that heating from 20 °C to 40 °C has no effect on the beet membranes.: Data never prove "no effect"; a small effect could exist that four cubes cannot detect.
• Reject it: the four 40 °C values include the highest single reading of the two groups, 0.12.: One high value is within the normal spread; it is not evidence of a real difference.

The lowest 80 °C value (0.81) is about seven times the highest 20 °C value (0.11). A gap that large, with no overlap, is very unlikely to arise by chance.

• Correct: Reject the null hypothesis: every 80 °C value is far above every 20 °C value, too large a gap to blame on chance.: Correct: reject the null; the data support the alternative.
• Fail to reject the null hypothesis: four cubes per group is too few to reach a decision about any difference in leakage.: Small samples can still show a clear difference when the gap is huge compared with the spread.
• Reject the alternative hypothesis: the 80 °C results are more spread out, so they are less reliable.: A slightly larger range does not cancel a difference this large.
• Prove the alternative hypothesis: the difference shows that heat causes leakage in beets of any variety or age.: Data support a hypothesis; they do not prove it for every case.

Membranes are phospholipid bilayers held together by weak hydrophobic interactions, studded with proteins whose shape depends on weak bonds. High temperature loosens the bilayer and denatures the proteins, so the barrier fails and the water-soluble red substance escapes.

• Correct: Heat disrupts the membrane: the bilayer becomes more fluid and membrane proteins unfold, opening gaps the red substance escapes through.: Correct: a disrupted barrier lets the substance out.
• Heat makes the red substance evaporate from the cells, and it then dissolves back into the water around the cubes.: The substance is dissolved in water inside the cells; it does not evaporate in 1 minute of heating.
• Heat makes the cell walls of the beet shrink, which squeezes the red substance out through the intact membranes.: Squeezing would not explain a jump in leakage; the membranes are the barrier that fails.
• Heat causes the beet cells to make more of the red substance, so the same undamaged membranes release a larger amount of it into the water.: One minute of heat does not make cells produce more substance; a damaged cell is not making anything.

The null says the independent variable (cholesterol) has no effect on the dependent variable (fluidity); the alternative says it does.

• Correct: H₀: adding cholesterol has no effect on membrane fluidity at 10 °C. H₁: adding cholesterol changes membrane fluidity at 10 °C.: Correct.
• H₀: adding cholesterol makes membranes less fluid at 10 °C. H₁: adding cholesterol makes membranes more fluid at 10 °C.: Both statements claim an effect; neither is a "no effect" null.
• H₀: cholesterol changes membrane fluidity at 10 °C. H₁: cholesterol has no effect on membrane fluidity at 10 °C.: This swaps the two.
• H₀: membranes are fluid at 10 °C. H₁: membranes are solid at 10 °C whether or not they contain cholesterol.: Neither statement is about the independent variable, cholesterol.

Without cholesterol the values run 1.9-2.3; with cholesterol 2.7-3.1. No overlap and a 0.8 µm²/s gap against ranges of 0.4 make chance an unlikely explanation.

• Correct: Reject the null hypothesis: the two groups do not overlap, and the difference in means is large compared with the spread.: Correct.
• Fail to reject the null hypothesis: cholesterol is known to stiffen membranes, so this result is a mistake.: Data are judged on what they show. At low temperature cholesterol keeps phospholipids from packing tightly, which raises fluidity; there is no reason to dismiss the result.
• Accept the null hypothesis: both groups of membranes were fluid, so cholesterol made no difference.: A null hypothesis is never accepted, and here the groups clearly differ.
• Fail to reject the null hypothesis: six membranes per group are too few to support any decision about the effect of cholesterol.: Six per group is enough when the groups do not overlap at all.

Only the independent variable (cholesterol) should differ. The phospholipids and the 10 °C temperature both affect fluidity, so they must be controlled.

• Correct: The kind of phospholipid and the temperature: Correct: both affect fluidity, so both are controlled.
• The amount of cholesterol in each membrane: Cholesterol is the independent variable; it is the one factor meant to differ.
• The speed at which the labeled lipid moved sideways: Sideways speed is the dependent variable, the measured result.
• The number of membranes, which could differ freely between the groups: Equal numbers of repeats are good practice, but the phrase "could differ freely" ignores that both groups had six; the factors that must match are those that affect fluidity.