AP Statistics øvingsprøve: enhet 1 til 5
- 15 spørsmål
- Cirka 15 min
- Gratis
Spørsmålene i testen er på engelsk.
A histogram of household incomes in a large city is strongly skewed to the right. Which statement is correct?
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Om denne testen
Dette er en gratis smakebit med 15 spørsmål i stil med flervalgsdelen av AP Statistics, skrevet av StudyPDF-teamet for kurset slik det er revidert for 2026-27. Den dekker alle de fem enhetene, fra data med én variabel og studiedesign via sannsynlighet og inferens for andeler og gjennomsnitt til regresjon, og blander flervalg, velg alle som passer og fyll inn luken. Svar på alle 15, sjekk så poengsummen din og les den gjennomgåtte forklaringen til hvert spørsmål.
Alle 15 spørsmål i oversikt
Vil du heller lese før du spiller? Alle spørsmålene i smakebiten står listet under. Svar og forklaringer er skjult til du åpner dem.
1.A histogram of household incomes in a large city is strongly skewed to the right. Which statement is correct?
- A. The mean is larger than the median, and the median is the better summary of a typical household
- B. The mean is smaller than the median, and the median is the better summary of a typical household
- C. The mean equals the median, so either one summarizes the center equally well
- D. The mean is larger than the median, and the mean is the better summary because it uses every value
Svar: A. The mean is larger than the median, and the median is the better summary of a typical household
In a right-skewed distribution the long tail of high values pulls the mean up toward the tail, while the median stays near the bulk of the data. So the mean is larger than the median. Because the mean is sensitive to those extreme values, the median describes a typical household better. Using every value is a weakness here, not a strength. The mean and median are about equal only for roughly symmetric distributions.
2.In the data set 3, 5, 6, 8, 9, 11, 12, the largest value is changed from 12 to 60. Which statistics stay the same?
Velg alle som passer.
- A. The median
- B. The interquartile range
- C. The standard deviation
- D. The range
- E. The mean
Svar: A. The median, B. The interquartile range
The median is the fourth value, 8, and it does not move. The first quartile is the median of 3, 5, 6, which is 5, and the third quartile is the median of the upper three values, 11 before and after the change, so the IQR is 6 both times. The mean jumps from 54/7 (about 7.7) to 102/7 (about 14.6), the range grows from 9 to 57, and the standard deviation grows a lot. Statistics built from the middle of the data are resistant to outliers, and statistics built from every value or from the extremes are not.
3.A county has 12 high schools. A researcher randomly selects 3 of the schools and surveys every student at those 3 schools. Which sampling method is this?
- A. Cluster sampling
- B. Stratified random sampling
- C. Simple random sampling
- D. Systematic sampling
Svar: A. Cluster sampling
The population is divided into natural groups (the schools), a random sample of whole groups is chosen, and every member of the chosen groups is surveyed. That is cluster sampling. In stratified sampling you would take some students from every group, which would mean visiting all 12 schools. A simple random sample would pick individual students from the whole county, and a systematic sample picks every kth name from a list.
4.A gardener wants to compare two fertilizers using 20 tomato plants. Ten of the plants are on the sunny side of a greenhouse and ten are on the shady side, and light is known to affect growth. Which design is best?
- A. Put every sunny plant on fertilizer A and every shady plant on fertilizer B
- B. Within the sunny plants and within the shady plants separately, randomly assign half to each fertilizer
- C. Let the gardener pick which fertilizer each plant gets
- D. Randomly assign fertilizers to all 20 plants and ignore the light difference
Svar: B. Within the sunny plants and within the shady plants separately, randomly assign half to each fertilizer
This is a randomized block design. Light is a known source of variation, so the plants are blocked by sun and shade, and the fertilizers are randomly assigned within each block. That way each fertilizer is tried equally in both light conditions and the effect of light is separated from the effect of fertilizer. The first option confounds fertilizer with light, the third invites bias, and the last one is valid but wastes the chance to remove the light variation.
5.Of 250 students surveyed, 40 play both a sport and an instrument, 90 play only a sport, 30 play only an instrument and 90 play neither. A student who plays an instrument is chosen at random. What is the probability that this student also plays a sport?
- A. 0.16
- B. 0.31
- C. 0.52
- D. 0.57
Svar: D. 0.57
The condition is that the student plays an instrument, so the sample space shrinks to the 40 + 30 = 70 instrument players. Of those, 40 also play a sport, so the probability is 40/70, about 0.57. The answer 0.31 is the reverse, 40/130, the chance that a sport player also plays an instrument. The answer 0.16 is 40/250, the chance of doing both, and 0.52 is 130/250, the chance of playing a sport at all.
6.Events A and B satisfy P(A) = 0.4, P(B) = 0.5 and P(A and B) = 0.2. Which statements are true?
Velg alle som passer.
- A. A and B are independent
- B. A and B are mutually exclusive
- C. P(A or B) = 0.7
- D. P(A given B) = 0.4
- E. P(A or B) = 0.9
Svar: A. A and B are independent, C. P(A or B) = 0.7, D. P(A given B) = 0.4
Independence means P(A and B) = P(A) times P(B), and 0.4 times 0.5 is 0.2, so A and B are independent. Equivalently, P(A given B) = 0.2/0.5 = 0.4, which equals P(A). For the union, P(A or B) = 0.4 + 0.5 - 0.2 = 0.7. Mutually exclusive events cannot happen together, so P(A and B) would be 0, but here it is 0.2. The value 0.9 forgets to subtract the overlap, which is counted twice.
7.Complete the sentence.
A basketball player makes 70 percent of free throws, and attempts are independent. The number of made shots in 10 attempts follows a binomial distribution with mean _____ and standard deviation about _____.
Alternativer for luke 1: 3, 7, 7.7, 10
Alternativer for luke 2: 2.1, 1.45, 2.65, 7
Svar: 7, 1.45
For a binomial random variable the mean is n times p = 10 times 0.7 = 7. The standard deviation is the square root of n times p times (1 - p) = sqrt(10 times 0.7 times 0.3) = sqrt(2.1), about 1.45. The value 2.1 is the variance, not the standard deviation, and 2.65 is sqrt(np), which forgets the (1 - p) factor.
8.In a random sample of 400 residents of a city, 220 support a new bus line. A 95% confidence interval for the proportion of all residents who support it is 0.501 to 0.599. Which interpretation is correct?
- A. We are 95% confident that the proportion of all residents who support the bus line is between 0.501 and 0.599
- B. 95% of the residents in the city support the bus line
- C. There is a 95% probability that a new sample proportion will fall between 0.501 and 0.599
- D. 95% of all possible samples have a sample proportion between 0.501 and 0.599
Svar: A. We are 95% confident that the proportion of all residents who support the bus line is between 0.501 and 0.599
A confidence interval is a statement about the population parameter, here the proportion of all residents. The 95% describes the method: if you repeated the sampling many times, about 95% of the intervals built this way would capture the true proportion. The interval says nothing about what percent of residents hold a view, and it is not a range for future sample proportions. Those would vary around the true value, not around this one sample's 0.55.
9.Complete the sentence.
In a random sample of 250 students, 90 own a bicycle. The sample proportion is _____, and the standard error of the sample proportion is about _____.
Alternativer for luke 1: 0.64, 0.36, 0.28, 90
Alternativer for luke 2: 0.48, 0.0009, 0.0304, 0.0608
Svar: 0.36, 0.0304
The sample proportion is p-hat = 90/250 = 0.36. The standard error is sqrt(p-hat times (1 - p-hat) / n) = sqrt(0.36 times 0.64 / 250) = sqrt(0.0009216), about 0.0304. The value 0.48 comes from forgetting to divide by n, 0.0009 is the variance, and 0.0608 is twice the standard error, roughly the margin of error for 95% confidence.
10.A researcher takes a separate random sample of 100 students from each of three schools and asks each student to choose a favorite lunch from four options. The goal is to decide whether the distribution of favorite lunch is the same at all three schools. Which test is appropriate, and what are its degrees of freedom?
- A. Chi-square test for independence, df = 6
- B. Chi-square test for homogeneity, df = 12
- C. Chi-square test for homogeneity, df = 6
- D. Chi-square test for independence, df = 11
Svar: C. Chi-square test for homogeneity, df = 6
Separate random samples were taken from each of several populations (the three schools) and one categorical variable was recorded, and the question is whether the distributions match. That is a test for homogeneity. Independence would apply to one random sample from one population with two categorical variables recorded. The table has 3 rows and 4 columns, so df = (3 - 1)(4 - 1) = 6. The number 12 is the count of cells, and 11 is one less than that.
11.A population has mean 50 and standard deviation 12. For random samples of size 36, what are the mean and standard deviation of the sampling distribution of the sample mean?
- A. Mean 50, standard deviation 12
- B. Mean 50, standard deviation 2
- C. Mean 50, standard deviation 0.33
- D. Mean 8.33, standard deviation 2
Svar: B. Mean 50, standard deviation 2
The sampling distribution of x-bar is centered at the population mean, 50, because the sample mean is an unbiased estimator. Its standard deviation is the population standard deviation divided by the square root of the sample size: 12/sqrt(36) = 12/6 = 2. The answer 0.33 divides by n instead of the square root of n. With n = 36 the shape is also close to normal even if the population is not, by the central limit theorem.
12.A 95% confidence interval for the difference in population means, mu_A - mu_B, based on two independent random samples, is (-1.2, 4.6). Which statements are justified?
Velg alle som passer.
- A. Zero is a plausible value for the difference in population means
- B. A two-sided test of H0: mu_A = mu_B at the 5% significance level would not reject H0
- C. There is a 95% probability that the difference in sample means is between -1.2 and 4.6
- D. The data prove that the two population means are equal
- E. The interval shows mean A is larger than mean B
Svar: A. Zero is a plausible value for the difference in population means, B. A two-sided test of H0: mu_A = mu_B at the 5% significance level would not reject H0
Because 0 lies inside the interval, a difference of 0 is a plausible value, and a two-sided test at the matching 5% level would not reject the null hypothesis of no difference. That is not the same as proving the means are equal. The data are simply not convincing evidence of a difference. The sample difference is the center of the interval and is known, so there is no probability statement to make about it. And since the interval includes negative values, it does not show that mean A is the larger one.
13.A least-squares line for predicting exam score from hours studied is: predicted score = 52 + 6.5(hours). Which is the correct interpretation of the slope?
- A. A student who studies 0 hours is predicted to score 6.5
- B. Every student who studies one more hour scores exactly 6.5 points higher
- C. 6.5 percent of the variation in exam scores is explained by hours studied
- D. For each additional hour studied, the predicted exam score increases by about 6.5 points
Svar: D. For each additional hour studied, the predicted exam score increases by about 6.5 points
The slope is the change in the predicted response for each one-unit increase in the explanatory variable, so each extra hour goes with about 6.5 more points on average. It describes the model's prediction, not a guarantee for each student, which rules out the second option. The intercept, 52, is the predicted score at 0 hours. The percent of variation explained is r squared, a different quantity.
14.Complete the sentence.
A linear model has a correlation of r = -0.80. About _____ percent of the variation in the response is explained by its linear relationship with the explanatory variable, and the slope of the least-squares line is _____.
Alternativer for luke 1: 8, 64, 80, 20
Alternativer for luke 2: positive, zero, negative, equal to -0.80
Svar: 64, negative
The proportion of variation explained is r squared: (-0.80) squared is 0.64, so about 64 percent. The slope always has the same sign as r, so a negative correlation means a negative slope. The slope is not equal to r in general, because it also depends on the ratio of the two standard deviations: slope = r times (s_y / s_x).
15.A least-squares line for predicting weight in kilograms from height in centimeters is: predicted weight = -12 + 0.5(height). A person who is 170 cm tall weighs 68 kg. What is the residual?
- A. 73 kg
- B. 5 kg
- C. -5 kg
- D. 68 kg
Svar: C. -5 kg
The predicted weight is -12 + 0.5(170) = 73 kg. A residual is the actual value minus the predicted value, so it is 68 - 73 = -5 kg. The negative sign means the line overestimates this person's weight. The value 73 is the prediction itself, and 5 kg has the sign reversed.
Slik er den reviderte AP Statistics-eksamenen bygd opp og vektet
AP Statistics-eksamenen gir en score fra 1 til 5 og ble revidert for skoleåret 2026-27, så den første eksamenen i det nye formatet er den i mai 2027. Ifølge College Board har del I 42 flervalgsspørsmål på 1 time og 30 minutter og del II 4 langsvarsspørsmål på 1 time og 30 minutter, og hver del utgjør 50 prosent av scoren. Hvert flervalgsspørsmål har nå 4 svaralternativer i stedet for 5, to sett på 3 spørsmål deler én felles tekst (ett om sannsynlighet og fordelinger, ett om regresjon), og hvert langsvarsspørsmål gir 10 poeng. Eksamenen er helt digital i Bluebook-appen, langsvarene medregnet, og kalkulator er tillatt. Øvingsprøver og repetisjonsbøker skrevet før revisjonen beskriver 40 spørsmål med 5 alternativer og 6 langsvarsspørsmål, så sjekk årstallet på alt du finner.
Kurset er nå fem enheter i stedet for ni, og College Board publiserer hvor stor del av eksamenscoren hver får. Utforsking av data med én variabel og innsamling av data utgjør 20 til 30 prosent, sannsynlighet, stokastiske variabler og sannsynlighetsfordelinger 15 til 25, inferens for kategoriske data (andeler) 15 til 25, inferens for kvantitative data (gjennomsnitt) 10 til 20, og regresjonsanalyse 10 til 20. Revisjonen tok også bort noen emner: kjikvadrattesten for tilpasning, den geometriske fordelingen, kombinasjon av stokastiske variabler og hele enheten om inferens for stigningstall. Kjikvadrattesten for homogenitet eller uavhengighet består. Hvis øvingsmaterialet ditt fortsatt har en oppgave om inferens for stigningstall eller tilpasningstest, er det fra det gamle kurset.
5 er toppscore, men hva en score er verdt, bestemmer hvert college. Noen gir studiepoeng for en 3, mange ber om en 4 eller en 5, og reglene varierer fra skole til skole. Sjekk collegene du bryr deg om før du bestemmer hvor hardt du vil satse.
Slik bruker du denne smakebiten, og slik tar du den på papir
De 15 spørsmålene er spredt over de fem enhetene, med fire på den tyngste, data med én variabel og studiedesign, og to på inferens for gjennomsnitt. De ber om begrunnelsen bak et resultat mer enn om regningen: hvorfor medianen er det beste sammendraget av en skjev fordeling, hvorfor blokkdesign slår et fullstendig randomisert design når en kjent faktor spiller inn, hva et konfidensnivå på 95 prosent faktisk hevder, hvorfor et konfidensintervall som inneholder 0 ikke beviser at to gjennomsnitt er like. Det er også det tankearbeidet langsvarsspørsmålene belønner.
Ta den i én økt med kladdepapir, og bruk kalkulator til de få kvadratrøttene, som på den ekte eksamenen. Les så forklaringen til hvert spørsmål, også de du fikk riktig. Behandle en bom som et tema. Bommet du på spørsmålet om konfidensintervall og spørsmålet om standardfeil, er hullet trolig hva en utvalgsfordeling er, ikke to separate formler. Matematikk er skrevet i ren tekst her, så p-hat betyr utvalgsandelen og x-bar betyr utvalgsgjennomsnittet.
Vil du heller jobbe på papir, bruk knappen for å laste ned prøven som PDF over spørsmålene. Filen har alle 15 spørsmålene med fasit på siste side og krever en gratis StudyPDF-konto. Spørsmålene er originale og skrevet etter det publiserte kursoppsettet. De er ikke frigitte eksamensspørsmål, og denne smakebiten øver ikke langsvarsdelen. Til den kan du gå gjennom College Boards frigitte langsvarsspørsmål, men husk at tidligere år bruker det gamle formatet med seks spørsmål. På et langsvarsspørsmål kommer poengene av å navngi metoden, sjekke vilkårene, gjøre utregningen og konkludere i sammenhengen.
Slik lager StudyPDF AP Statistics-prøver fra klassenotatene dine
Femten spørsmål kan vise deg hvilken enhet som er ustabil. De gjør deg ikke klar alene, og en generell spørsmålsbank passer sjelden til datasettene, skrivemåten og eksemplene læreren din faktisk bruker.
StudyPDF tar i stedet utgangspunkt i ditt materiale. Last opp kapitlene fra læreboka, lærerens lysbilder, et gjennomgått oppgavesett eller repetisjonsheftet, trykk Nytt materiale, og StudyPDF lager øvingsprøver fra akkurat de sidene. Hvert spørsmål bygger på materialet ditt, og hver forklaring viser hvor svaret kommer fra, så du kan gå rett tilbake til siden når et trinn ikke henger sammen.
Du trenger ikke laste opp noe for å begynne. Nevn heller et tema, for eksempel konfidensintervall for en andel eller kjikvadrattesten, så setter Bo det opp med nøkkelbegrepene, og du kan lage quizer og flashcards på det. Resultatene dine viser hvilke begreper du stadig bommer på, så neste øvingsprøve kan ta sikte på dem. Det er gratis å starte.
Skrevet av StudyPDF-teamet. Sist oppdatert 19. august 2026.
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Er denne AP Statistics-øvingsprøven gratis?
Ja. Alle 15 spørsmålene, poengskjermen og hver gjennomgåtte forklaring er gratis, og quizen kjører i nettleseren din. En gratis StudyPDF-konto trenger du for å laste ned prøven som PDF med fasit eller for å lage flere øvingsprøver fra egne notater.
Hvem har skrevet disse spørsmålene?
StudyPDF-teamet har skrevet alle spørsmål og forklaringer etter de fem enhetene i det publiserte AP Statistics-kursoppsettet for 2026-27. Det er originale oppgaver, ikke ekte eller frigitte eksamensspørsmål, og StudyPDF er ikke tilknyttet College Board, som ikke støtter denne siden.
Stemmer dette med det reviderte kurset for 2026-27?
Ja. Den bruker oppsettet med fem enheter og lar de emnene College Board har tatt bort, ligge, blant dem inferens for stigningstall og kjikvadrattesten for tilpasning. Den ekte flervalgsdelen har nå 4 alternativer per spørsmål og ett riktig svar. Denne smakebiten bruker også velg alle som passer og fyll inn luken, fordi det å vurdere hvert alternativ for seg er en god sjekk på en enhet. Den øver ikke de fire langsvarsspørsmålene.
Kan jeg få øvingsprøver laget fra mitt eget klassemateriale?
Ja. Last opp kapitlene fra læreboka, lysbilder, oppgavesett eller repetisjonshefte til StudyPDF, så kan du lage øvingsprøver fra akkurat de sidene, med forklaringer knyttet til kildene dine. Har du ingenting å laste opp, kan du nevne et tema eller en enhet i stedet.