Take this Quiz: AP Statistics — collecting data | Zestly

Question 1

In an invented study, five hundred employees are drawn at random from a firm of five thousand and asked about a proposed change to working hours; sixty-two per cent of those asked are in favour. Suppose that across the whole firm the figure is fifty-eight per cent. Which number is the parameter and which the statistic?

Accepted Answer

Fifty-eight per cent is the parameter and sixty-two per cent is the statistic

Answer

Both figures are statistics, since both were obtained by counting people

Answer

Both figures are parameters, since both describe the same firm

Answer

Sixty-two per cent is the parameter and fifty-eight per cent is the statistic

Question 2

In an invented case, a cafe owner wants to know whether her customers prefer a new coffee blend. She stands at the door during the morning rush and asks the first fifty people who come in. Why is the result likely to mislead her, and what would a larger version of the same survey achieve?

Accepted Answer

Morning customers may differ systematically from afternoon and evening ones, so the sample tilts in a particular direction — and asking more people in the same way would measure that tilted group more precisely without correcting it

Answer

No margin of error can be computed from fifty people, so the result carries no information of any kind

Answer

Fifty is below the threshold at which a normal approximation may be used, which is the whole of the difficulty

Answer

The sample is too small; asking five hundred morning customers the same way would fix the problem

Question 3

In an invented survey, a district containing ten schools picks two schools at random and surveys every pupil in those two. Which method is this, and how would the alternative have been carried out?

Accepted Answer

Cluster sampling; a stratified design would instead have drawn a random sample of pupils from within EVERY school

Answer

Simple random sampling; the alternative would have been to number all pupils in the district and draw names at random

Answer

Stratified sampling; the alternative would have been to survey every pupil in every school

Answer

Systematic sampling; the alternative would have been to pick a random starting pupil and then every tenth name on the roll

Question 4

In an invented factory an inspector checks every twentieth item coming off a line. Under what circumstance would that produce a systematically unrepresentative sample?

Answer

If the total number of items made in a shift is not an exact multiple of twenty

Answer

If the inspector begins at the first item rather than choosing a starting point at random among the first twenty

Answer

If the line runs quickly, since items would then pass the station faster than they can be judged

Answer

If the process repeats on a cycle whose length divides into twenty — for instance four machines feeding the line in rotation, so that every twentieth item always comes from the same one

Question 5

An invented national survey is conducted by telephoning landlines during working hours. Of those reached, about a fifth agree to take part. Which description names the UNDERCOVERAGE in that design, as distinct from its other problems?

Answer

Four fifths of those reached declined, and people who decline may differ from people who agree

Answer

Working hours were chosen, so those at work were harder to reach than those at home

Answer

Households without a landline had no chance of being selected at all, so they are absent from the list the sample was drawn from

Answer

The wording of the questions may have pushed respondents towards particular answers