SAT MAth Practice questions – all topics
- Problem-solving and Data Analysis Weightage: 15% Questions: 5-7
- Ratios, rates, proportional relationships, and units
- Percentages
- One-variable data: distributions and measures of centre and spread
- Two-variable data: models and scatterplots
- Probability and conditional probability
- Inference from sample statistics and margin of error
- Evaluating statistical claims: observational studies and Experiments
SAT MAth and English – full syllabus practice tests
Question Hard
Micha and Rana each selected a random sample of students at their school and asked how many soft drink servings each student had consumed the previous week. Micha estimated that the mean number of soft drink servings was 7.1 , with an associated margin of error of 1.2. Rana estimated that the mean number of soft drink servings was 8.3 , with an associated margin of error of 0.8 . Assuming the margins of error were calculated in the same way, which of the following best explains why Rana obtained a smaller margin of error than Micha?
A. Rana’s sample contained more students than Micha’s sample contained.
B. Rana’s sample contained more students who drink soft drinks than Micha’s sample contained.
C. Rana’s sample contained more students who drank exactly seven soft drink servings than Micha’s sample contained.
D. Rana’s sample contained more students who drank exactly eight soft drink servings than Micha’s sample contained.
▶️Answer/Explanation
Ans:A
To determine why Rana obtained a smaller margin of error than Micha, we need to understand how margins of error are calculated and how they relate to sample size.
The margin of error (ME) for a sample mean is typically calculated using the formula:
\[ ME = z \times \frac{\sigma}{\sqrt{n}} \]
Where:
\( z \) is the z-score corresponding to the desired level of confidence (usually based on the standard normal distribution).
\( \sigma \) is the population standard deviation (if known).
\( n \) is the sample size.
Since both margins of error were calculated in the same way, we can infer that the difference in their margins of error is likely due to a difference in sample size \( n \).
Option A: Rana’s sample contained more students than Micha’s sample contained.
This is a plausible explanation. A larger sample size generally leads to a smaller margin of error. More data points allow for a more accurate estimation of the population mean.
Options B, C, and D involve the distribution of soft drink servings among the samples, which may influence the mean but not necessarily the margin of error. Therefore, they are less likely to explain the difference in margins of error.
Question Hard
Two different store owners in a shopping center estimated the percentage of all visitors who wear eyeglasses. They each selected a random sample of the shopping center visitors and recorded whether the visitors were wearing eyeglasses. The results from each sample are shown in the table below.
If the associated margin of error was calculated the same way for both samples, which of the following is the most likely reason that the result for Sample A has a larger margin of error?
A)Sample A included more visitors than Sample B.
B)Sample B included more visitors than Sample A.
C)Sample A included a greater percentage of visitors who were wearing eyeglasses than Sample B.
D)Sample B included a greater percentage of visitors who were wearing eyeglasses than Sample A.
▶️Answer/Explanation
B)Sample B included more visitors than Sample A.
The margin of error in a survey result is influenced by several factors, including the sample size. When the margin of error is calculated the same way for different samples, a larger margin of error typically indicates a smaller sample size. This is because the margin of error decreases as the sample size increases, due to the reduced variability in the estimate.
Given that the percentages of visitors wearing eyeglasses are the same (21%) in both samples but the margin of error differs (3% for Sample A and 2% for Sample B), the most likely reason for the larger margin of error in Sample A is that it included fewer visitors than Sample B.
Therefore, the correct answer is:
B) Sample B included more visitors than Sample A.
Questions
$\frac{2}{x-2}+\frac{3}{x+5}=\frac{r x+t}{(x-2)(x+5)}$
The equation above is true for all $x>2$, where $r$ and $t$ are positive constants. What is the value of $r t$ ?
A. -20
B. 15
C. 20
D. 60
▶️Answer/Explanation
Ans: C
Questions
37.
The table above shows the recommended amount of potassium, in milligrams (mg) per day, for people of all ages according to the National Academy of Medicine.
Andrea’s recommended daily intake of potassium is 50% greater than that of her two-year-old brother. What is the least possible age, in years, of Andrea? 1.3
▶️Answer/Explanation
Ans: 9