Statistical Experiments, Simulation and Decisions: Algebra 2 Math Test – PDF Download

Question 1: Spinner claim (2 points)

A spinner is labeled so that green should come up with probability \(0.2\). Ayla spins it \(40\) times and gets green \(15\) times . The histogram shows \(100\) simulated sets of \(40\) spins with \(P(\text{green})=0.2\).

1. Find the expected number of green results in \(40\) spins. (1 point)
2. Use the simulation to decide whether Ayla’s result is consistent with the claim. (1 point)

Question 2: Marbles with no red (2 points)

A bag is said to have \(25\%\) red marbles. A student draws \(8\) marbles one at a time, replacing each, and gets no red marbles.

1. Assuming the claim is true, find the probability of no red marble in \(8\) draws. (1 point)
2. Decide whether the result is consistent with the claim and justify the decision. (1 point)

Question 3: Assign groups at random (2 points)

A teacher has \(14\) volunteers and wants \(7\) to take a quiz with music and \(7\) in silence.

1. Describe a procedure that randomly assigns the volunteers. (1 point)
2. Explain why random assignment makes a fair comparison. (1 point)

Question 4: Music and quiz scores (3 points)

The \(12\) volunteers in a study were randomly assigned, six to study with music and six in silence. Their quiz scores (out of \(20\)) are shown. The scores were pooled and randomly split into two groups of six \(1{,}000\) times ; 37 splits gave a difference of means of \(2\) or more (Music minus Silence).

1. Find each group’s mean and the difference. (1 point)
2. Estimate the probability of a difference at least this large by chance. (1 point)
3. State whether the result is statistically significant at the \(5\%\) level and what it means. (1 point)

Question 5: Kinds of studies (2 points)

For each study, state whether it is an experiment or an observational study and whether it can show cause and effect.

1. Fifty plots of land are randomly assigned to one of two fertilizers, and crop yields are compared. (1 point)
2. A school compares grades of students who play an instrument with grades of students who do not. (1 point)

Question 6: Doubling headline (2 points)

A news site shows this graph.

1. Find the actual percent increase in subscribers from 2022 to 2023. (1 point)
2. Explain why the graph is misleading. (1 point)

Question 7: Choose one of four (2 points)

Four friends want to use one standard die to choose a winner fairly, rolling again when needed.

1. Describe how to assign the die faces. (1 point)
2. Find the probability that the winner is decided on the first roll. (1 point)

Question 8: Carnival wheel (3 points)

A carnival game costs \(\$2\) to play. A wheel pays \(\$10\) with probability \(0.1\), pays \(\$3\) with probability \(0.2\), and pays nothing otherwise.

1. Find the expected payout of one play. (1 point)
2. Find the expected net result per play for the player. (1 point)
3. Decide whether the game is fair and find a price that would make it fair. (1 point)

Question 9: Scanner flags (2 points)

A scanner checks items at a factory. The tree diagram shows the probabilities.

1. Find the probability that a random item is flagged. (1 point)
2. Find the probability that a flagged item is defective. (1 point)

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