AP Statistics-øveprøve: enhed 1 til 5
- 15 spørgsmål
- Cirka 15 min.
- Gratis
Testens spørgsmål 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 test
Det her er en gratis smagsprøve på 15 spørgsmål i stil med multiple choice-delen af AP Statistics, skrevet af StudyPDF-teamet til kurset, som det er revideret til 2026-27. Den dækker alle fem enheder, fra data med én variabel og undersøgelsesdesign over sandsynlighed og inferens for andele og gennemsnit til regression, og den blander multiple choice, vælg alle der passer og udfyld det tomme felt. Svar på alle 15, se så din score og læs den gennemregnede forklaring til hvert spørgsmål.
Alle 15 spørgsmål i overblik
Vil du hellere læse, før du går i gang? Alle spørgsmål i smagsprøven står herunder. Svar og forklaringer er foldet sammen, indtil du åbner 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?
Vælg alle, der 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?
Vælg alle, der 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 _____.
Muligheder for felt 1: 3, 7, 7.7, 10
Muligheder for felt 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 _____.
Muligheder for felt 1: 0.64, 0.36, 0.28, 90
Muligheder for felt 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?
Vælg alle, der 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 _____.
Muligheder for felt 1: 8, 64, 80, 20
Muligheder for felt 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.
Hvordan den reviderede AP Statistics-eksamen ser ud, og hvordan den vægtes
AP Statistics-eksamen scores fra 1 til 5 og blev revideret til skoleåret 2026-27, så den første eksamen i det nye format er den i maj 2027. Ifølge College Board er Del I 42 multiple choice-spørgsmål på 1 time og 30 minutter, og Del II er 4 frie besvarelser på 1 time og 30 minutter, og hver del tæller 50 procent af scoren. Hvert multiple choice-spørgsmål har nu 4 svarmuligheder i stedet for 5, to sæt på 3 spørgsmål deler én opgavetekst (det ene om sandsynlighed og fordelinger, det andet om regression), og hvert spørgsmål i de frie besvarelser er 10 point værd. Eksamen er fuldt digital i appen Bluebook, de frie besvarelser inklusive, og lommeregner er tilladt. Øveprøver og repetitionsbøger skrevet før revisionen beskriver 40 spørgsmål med 5 svarmuligheder og 6 frie besvarelser, så tjek årstallet på alt, du finder.
Kurset består nu af fem enheder i stedet for ni, og College Board offentliggør, hvor meget af eksamensscoren hver af dem får. Udforskning af data med én variabel og dataindsamling er 20 til 30 procent, sandsynlighed, stokastiske variable og sandsynlighedsfordelinger 15 til 25, inferens for kategoriske data (andele) 15 til 25, inferens for kvantitative data (gennemsnit) 10 til 20 og regressionsanalyse 10 til 20. Revisionen fjernede også nogle emner: chi-i-anden-testen for tilpasning, den geometriske fordeling, kombination af stokastiske variable og hele enheden om inferens for hældninger. Chi-i-anden-testen for homogenitet eller uafhængighed bliver. Hvis dit øvemateriale stadig har en opgave om hældningsinferens eller tilpasningstest, stammer den fra det gamle kursus.
En 5'er er den højeste score, men hvad en score er værd, afgør hvert college selv. Nogle giver merit for et 3-tal, mange kræver et 4 eller et 5, og politikken varierer fra skole til skole. Slå de colleges op, du interesserer dig for, før du beslutter, hvor hårdt du vil presse.
Sådan bruger du smagsprøven, og hvordan du tager den på papir
De 15 spørgsmål er spredt over de fem enheder med fire på den tungeste, data med én variabel og undersøgelsesdesign, og to på inferens for gennemsnit. De beder om begrundelsen bag et resultat mere end om regnestykket: hvorfor medianen er det bedre mål for en skæv fordeling, hvorfor blokering slår et fuldstændigt randomiseret design, når en kendt faktor betyder noget, hvad et konfidensniveau på 95 procent faktisk påstår, hvorfor et konfidensinterval, der indeholder 0, ikke beviser, at to gennemsnit er ens. Det er også den tænkning, de frie besvarelser giver point for.
Tag den i ét stræk med kladdepapir, og brug en lommeregner til de få kvadratrødder, som du ville gøre til den rigtige eksamen. Læs så forklaringen til hvert spørgsmål, også dem du svarede rigtigt på. Behandl en fejl som et emne. Hvis du missede spørgsmålet om konfidensintervaller og spørgsmålet om standardfejl, er hullet nok, hvad en stikprøvefordeling er, ikke to adskilte formler. Matematik er skrevet som ren tekst her, så p-hat betyder stikprøveandelen, og x-bar betyder stikprøvegennemsnittet.
Hvis du hellere vil arbejde på papir, så brug knappen Hent prøven som PDF over spørgsmålene. Filen har alle 15 spørgsmål med et facit på sidste side og kræver en gratis StudyPDF-konto. Spørgsmålene er originale og skrevet efter den offentliggjorte kursusbeskrivelse. De er ikke frigivne eksamensspørgsmål, og smagsprøven træner ikke delen med frie besvarelser. Til dem kan du arbejde med College Boards frigivne frie besvarelser, men husk, at tidligere år bruger det gamle format med seks spørgsmål. I de frie besvarelser kommer pointene fra at navngive proceduren, tjekke betingelserne, lave beregningen og konkludere i sammenhængen.
Sådan bygger StudyPDF AP Statistics-øveprøver ud fra dine noter fra timerne
Femten spørgsmål kan vise dig, hvilken enhed der er usikker. De kan ikke gøre dig klar alene, og en generisk spørgsmålsbank rammer sjældent de datasæt, den notation og de eksempler, din lærer faktisk bruger.
StudyPDF tager i stedet udgangspunkt i dit materiale. Upload dine lærebogskapitler, din lærers slides, et gennemregnet opgavesæt eller dit repetitionshæfte, tryk på Nyt materiale, og StudyPDF bygger øveprøver ud fra præcis de sider. Hvert spørgsmål bygger på dit materiale, og hver forklaring henviser til, hvor svaret kommer fra, så du kan gå direkte tilbage til siden, når et trin ikke giver mening.
Du behøver ikke uploade noget for at komme i gang. Nævn i stedet et emne, for eksempel konfidensintervaller for en andel eller chi-i-anden-testen, så sætter Bo det op med dets nøglebegreber, og du kan bygge quizzer og flashcards ud fra det. Dine resultater følger, hvilke begreber du bliver ved med at misse, så den næste øveprøve kan målrettes dem. Det er gratis at starte.
Skrevet af StudyPDF-teamet. Sidst opdateret 19. august 2026.
Godt at vide
Er denne AP Statistics-øveprøve gratis?
Ja. Alle 15 spørgsmål, scoreskærmen og hver gennemregnet forklaring er gratis, og quizzen kører i din browser. En gratis StudyPDF-konto skal du bruge for at hente prøven som PDF med facit eller for at bygge flere øveprøver ud fra dine egne noter.
Hvem har skrevet spørgsmålene?
StudyPDF-teamet har skrevet hvert spørgsmål og hver forklaring efter de fem enheder i den offentliggjorte AP Statistics-kursusbeskrivelse for 2026-27. Det er originale opgaver, ikke rigtige eller frigivne eksamensspørgsmål, og StudyPDF er ikke tilknyttet College Board, som ikke støtter denne side.
Passer den til det reviderede kursus 2026-27?
Ja. Den bruger strukturen med fem enheder og udelader de emner, College Board har fjernet, blandt andet inferens for hældninger og chi-i-anden-testen for tilpasning. Den rigtige multiple choice-del har nu 4 svarmuligheder per spørgsmål og ét rigtigt svar. Denne smagsprøve bruger også vælg alle der passer og udfyld det tomme felt, fordi det at bedømme hver mulighed for sig er en god kontrol af en enhed. Den træner ikke de fire frie besvarelser.
Kan jeg få øveprøver bygget ud fra mit eget klassemateriale?
Ja. Upload dine lærebogskapitler, slides, opgavesæt eller dit repetitionshæfte til StudyPDF, så kan du bygge øveprøver ud fra præcis de sider, med forklaringer knyttet til dine kilder. Har du ikke noget at uploade, så nævn et emne eller en enhed i stedet.