A town's records show that ice cream sales and pool rescues both rise every July and fall every October. What do these data establish?

City records show that the more firefighters sent to a fire, the greater the dollar damage. What best explains this pattern?

A survey shows that students who sleep more hours score higher on a math test. Which plan would give the best evidence that extra sleep causes higher scores?

A gardener gives a new plant food to 10 tomato plants, and they grow taller than last year's plants did. What is missing before he can claim the food caused the growth?

Students test whether water temperature changes how fast sugar dissolves. They stir 5 g of sugar into 100 mL of water at 10 C, 30 C and 50 C and time each cup. What is the independent variable?

Three 200 mL cups of water start at 20 C in sunlight for 2 hours. One is wrapped in foil, one in cloth, and one is left bare. What was held constant in this test?

Five timed trials of 10 pendulum swings give 12.1 s, 12.0 s, 12.2 s, 7.4 s and 12.1 s. What most likely explains the fourth trial?

A class counts sprouted seeds five separate times and reports the mean instead of one count. What does this practice mainly improve?

Beach town records show that as sunscreen sales rise, the number of sunburns treated at the clinic also rises. What third variable best explains both?

Twenty identical plants were grown under the same light and water. The 10 given fertilizer reached a mean height of 24 cm. The 10 without it reached 18 cm. What conclusion do these data support?

A company claims its sports drink causes faster recovery because drinkers reported feeling better afterwards. What evidence would most weaken that claim?

Two websites describe a new water filter. One is the maker's advertisement with no data. The other is a university lab report showing measured test results. Which source is more credible, and why?

A survey finds that students who join the school band earn higher grades. The principal says band raises grades. What is another reasonable explanation of the same pattern?

A class records screen time and sleep for four students: 1 h screen and 9.0 h sleep, 3 h and 8.2 h, 5 h and 7.1 h, 7 h and 6.3 h. What pattern do these data show?

Students notice that classrooms with more potted plants have lower measured noise levels. What extra evidence would best test whether the plants cause the quiet?

A student wants to know whether a fertilizer makes bean plants grow faster, so she changes only the fertilizer amount and keeps light, water and soil the same. What type of investigation is this?

A student writes: Claim, warm water dissolves sugar faster. Evidence, sugar dissolved in 20 s at 50 C and in 61 s at 10 C. What is missing from this argument?

A line graph showing two measurements rising together proves that one of them causes the other.

A control group lets scientists compare a treated group with an untreated group that was kept under the same conditions.

A pattern between two sets of data can be produced by a third variable that no one measured.