Flashcards
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Cards in this deck (26)
- 1When is it acceptable to remove an outlier in a dataset before proceeding with further analysis?When the outlier is clearly a mistake and you don't know how to retrieve the correct value.
- 2A CBS news poll conducted directly after the second presidential debate asked a random sample of 525 uncommitted voters who they thought won the debate. A 95% confidence interval for the percent of all U.S. uncommitted voters who thought Obama won is (33%, 41%). A correct interpretation of the confidence level is:In 95% of all random samples of size 525, the interval calculated from that sample will contain the true percent who thought Obama won.
- 3A pollster is designing a poll for the upcoming primary election. She wants to be able to report her results with a margin of error of error of 3.5%. What is the smallest sample size she can use?817
- 4Which of the following provides the most information about the shape of a data set?A. Five number summary
B. Boxplot
C. Pie chart
(D). Stem-and-leaf plot - 5An observational study is done to see if eating at least two apples a week helps prevent tooth decay in children. However, the researchers are aware that children who eat apples may also drink less soda, so they measure soda consumption as well. In this example, soda consumption is an example ofa confounding variable. ✅
Explanation: A confounding variable is an outside factor that may affect both the explanatory variable (apple consumption) and the response variable (tooth decay). In this case, children who eat more apples might also drink less soda, and soda consumption itself can affect tooth decay. Measuring soda consumption helps account for this potential confounder. - 6A company wants to test the reaction to its new microwave popcorn. It sends out free samples to 2500 randomly selected households and asks respondents to return the enclosed postcard with comments. Only 40% of the sample returns the postcard and of those, 80% are over 55 years old. The over-55 group is suspected to have a different opinion than the under-55 age group. This is an example of:non-response bias. ✅
Explanation: Non-response bias occurs when a significant portion of the selected sample does not respond, and the responses that are received are not representative of the entire sample. In this example, only 40% of households returned the postcard, and most of those respondents were over 55, which may skew the results because their opinions might differ from the under-55 group. - 7Two variables in a study are said to be confounded if:. one cannot separate their effects on a response variable ✅
Explanation: Two variables are confounded when their individual effects on the response variable cannot be distinguished from each other. This means it’s unclear whether the response is due to one variable, the other, or both together. Confounding can lead to misleading conclusions if not properly accounted for. - 8A central concern in an observational study is:not obtaining a large enough sample
- 9Which of the following is a true statement about sampling error? a. sampling error can be eliminated only if a survey is both extremely well designed and well conducted. b. sampling error reflects natural variation between samples, is always present, and can be described using probability. C. sampling error is generally larger when the sample size is larger. d. sampling error implies an error, possibly very small, but still an error on the part of the surveyor.sampling error reflects natural variation between samples, is always present, and can be described using probability
- 10In a linear regression situation, an outlier that fits the pattern of the rest of the data (i.e. is close to the line found using the rest of the data) will:increase the correlation but not change the regression line much. ✅
- 11In a 2-way table of categorical data: A. the explanatory variable is shown in the rows, the response variable is in the columns. B. the explanatory variable is shown in the columns, the response variable is in the rows. C. it doesn't matter which is put where- either way is OK.A. the explanatory variable is shown in the
rows, the response variable is in the
columns. - 12An instructor is teaching two Stats 7 summer classes. On one exam, the 32 students in the first class averaged 82, while the 48 students in the second class averaged only 77. If the instructor combines the classes to figure grades, what will the average exam score be? a. 78.5 b. 79 c. 79.5 d. 80 e. more information is neededTo find the combined average, we use a weighted average based on the number of students in each class.
Combined average
=
(
32
⋅
82
)
+
(
48
⋅
77
)
32
+
48
Combined average=
32+48
(32⋅82)+(48⋅77)
Step-by-step:
32
⋅
82
=
2624
32⋅82=2624
48
⋅
77
=
3696
48⋅77=3696
Sum:
2624
+
3696
=
6320
2624+3696=6320
Total students:
32
+
48
=
80
32+48=80
Combined average:
6320
/
80
=
79
6320/80=79
✅ Correct answer: b. 79 - 13In a study of winning percentages in home games vs. average home attendance for baseball games, the regression equation is: predicted winning % = 44 + 0.0003(attendance) What is the residual if a team has a winning % of 55% with an average attendance or 34,000?We can calculate the residual using the formula:
[
\text{residual} = \text{observed value} - \text{predicted value}
]
Step 1: Compute the predicted winning %
[
\text{predicted winning %} = 44 + 0.0003 \cdot 34,000
]
[
0.0003 \cdot 34,000 = 10.2
]
[
44 + 10.2 = 54.2
]
Step 2: Compute the residual
[
\text{residual} = 55 - 54.2 = 0.8
]
✅ Correct answer: C. 0.8 - 14Which of the following graphical methods cannot be used on a categorical data set? A. a stem-and-leaf display B. a pie chart C. a bar chart D. all of the above methods can be used on a categorical data setThe correct answer is:
**A. a stem-and-leaf display** ✅
**Explanation:** Stem-and-leaf displays are designed for **quantitative (numerical) data**, not categorical data. Pie charts and bar charts, on the other hand, are suitable for visualizing categorical data by showing the distribution of categories. - 15Which of the following two measures for a set of (x, y) values will always have the same sign as each other (both positive or both negative)? A. The intercept and slope of the regression line. B. The intercept of the regression line and the correlation. C. The slope of the regression line and the correlation. D. None of the above.The correct answer is:
**C. The slope of the regression line and the correlation.** ✅
**Explanation:** The slope of the regression line and the correlation coefficient **both reflect the direction of the linear relationship** between (x) and (y). If the correlation is positive, the slope is positive; if the correlation is negative, the slope is negative. The intercept, however, can be positive or negative regardless of the correlation or slope. - 16For this pair of variables, is there likely to be a positive association, a negative association, or no association? Briefly explain your reasoning: height and grade point average for college students a. We expect a negative association since we would expect taller college students to have higher grade point averages. b. We expect a positive association since we would expect taller college students to have lower grade point averages. c. We expect a positive association since we would expect taller college students to have higher grade point averages. d. We expect a negative association since we would expect taller college students to have lower grade point averages. e. No association would be expected between height and grade point average because the value of one variable is unlikely to affect the value of the other.The correct answer is:
**e. No association would be expected between height and grade point average because the value of one variable is unlikely to affect the value of the other.** ✅
**Explanation:** Height and GPA are unrelated traits. There is no logical reason to expect that taller students would have higher or lower GPAs, so we would generally expect **no association** between these two variables. - 17Two quantitative variables x and y have a positive association when A. the values of x tend to increase as the values of y increase. B. the values of x tend to decrease as the values of y increase. C the values of × tend to increase regardless of how the values of y change. D. the values of both x and y are always positive.The correct answer is:
**A. the values of x tend to increase as the values of y increase.** ✅
**Explanation:** A positive association means that **as one variable increases, the other variable also tends to increase**. This is the defining characteristic of a positive relationship between two quantitative variables. - 18Which of the following (measured on everyone in a large population of people) cannot have a bell- shaped distribution? A. the amount of sleep a person got last night B. whether or not a person smokes C. a person's resting heart rate D. a person's head circumferenceThe correct answer is:
**B. whether or not a person smokes** ✅
**Explanation:** A bell-shaped (normal) distribution applies to **quantitative variables** that can take many values and cluster around a mean. “Whether or not a person smokes” is a **categorical variable** (yes/no), so it cannot have a bell-shaped distribution. The other options—sleep hours, resting heart rate, and head circumference—are quantitative and could approximate a normal distribution. - 19Suppose you were to read about a study showing that people who sleep less than five hours a night have twice as much risk of a premature death as people who sleep seven or eight hours a night. Can you conclude that sleeping the shorter hours causes a higher risk of premature death? A. Yes, because the result was clearly based on a randomized experiment. B. No, because the result was clearly based on an observational study. C. The answer depends on whether the research was based on an observational study or a randomized experiment, and it isn't obvious which was used.The correct answer is:
**C. The answer depends on whether the research was based on an observational study or a randomized experiment, and it isn't obvious which was used.** ✅
**Explanation:** Causation can only be established through a **randomized experiment**. If the study was observational, we can only say there is an **association** between short sleep and higher risk of premature death. Without knowing the study design, we cannot conclude causation. - 20In 2017, the distribution of forced fumbles for the 32 NFL teams had a mean of 14.5 and a median of 13.5. The Chicago Bears were recorded as having 17 forced fumbles. An error was discovered- the Bears only had 14 fumbles. If that number is corrected, how would the mean and median be affected? a. The mean would decrease, while the median would increase. b. The mean would decrease, while the median would be unchanged. C. The mean would increase, while the median would be unchanged. d. Both would remain the same as before.The correct answer is:
**b. The mean would decrease, while the median would be unchanged.** ✅
**Explanation:** Correcting the Bears’ value from 17 to 14 lowers the total sum of forced fumbles, which **decreases the mean**. However, the median depends on the middle values of the ordered data, and changing one value from 17 to 14 **does not affect the middle value**, so the median remains **unchanged**. - 21Suppose the average score on a national test is 500 with a standard deviation of 100. If each score is increased by 50, what are the new mean and standard deviation? a. mean = 500 and SD = 100 b. mean = 500 and SD = 150 C mean = 550 and SD = 100 d. mean = 550 and SD = 150C
mean = 550 and SD = 100 - 22Two quantitative variables x and y have a positive association whenthe values of x tend to increase as the values of y increase. ✅
- 23You are taking a flight, and if it arrives more than 30 minutes late you will miss your connection. Otherwise, you will not miss your connection. tvent A = Flight arrives early or on time Event b = You miss vour connection Which of these is true about events A and B?Event A: Flight arrives early or on time.
Event B: You miss your connection (which happens only if the flight arrives more than 30 minutes late).
If the flight is on time or early (A), then you will not miss your connection (not B).
If the flight is more than 30 minutes late (B), it is not on time or early (not A).
✅ That means A and B cannot both happen → they are mutually exclusive.
But they don’t cover every possibility, because the flight could also be a little late (less than 30 minutes), which is not A and not B.
So they’re mutually exclusive, but not complements (since there’s a middle case).
Answer: C. They are mutually exclusive, but not complements. - 24Consider the following table of ages of U.S. senators: Age (VT): <40 40-40 50-59 60-69 70-79 Number of senators: What is the probability that a senator is under 70 years old, given that he or she is at least 50 years old? a. 0.580 b. 0.624 c. 0.643 d. 0.8920.892
- 25Suppose you toss a fair coin ten times, and it comes up heads every time. Which of the following is a true statement? a. by the law of large numbers, the next toss is more likely to be tails than another head. by the properties of conditional probability, the next toss is more likely to be a head given that ten tosses in a row have been heads. c. the law of large numbers tells how many tosses will be necessary before the percentages of heads and tails are again in balance. d. the probability that the next toss will again be a head is 0.5the probability that the next toss will again be a head is 0.5
- 26Prior to the 2020 election, Quinnnipiac University did a poll examining the extent to which independent voters supported Biden or Trump. A table of their results is shown below. Find the chi-square test statistic for this situation. Is there statistically significant evidence that voter affiliation and Trump-Biden support are independent?X2 = 1.12, not statistically significant
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- Flashcards on clicker , created by Brook Waters on 28/10/2025.
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