Quiz CHAPTER 10 Name:

  1. Explain the difference between a statistical relationship and a deterministic relationship.

Answer: in a deterministic relationship, if we know the value of one variable, we can determine the value of the other exactly. In a statistical relationship, natural variability exists in both measurements; we can talk about average relationships, not exact ones.

  1. Correlation measures the strength of a certain type of statistical relationship between two variables. What type(s) of variables can the two variables be?

Answer: two measurement variables.

  1. Assuming there is a statistical relationship between height and weight for adult females, which of the following statements is true?
  2. If we knew a woman’s height, we could predict her weight.
  3. If we knew a woman’s height, we could determine the exact weight for all women with that same height.
  4. If we knew a woman’s height, we could predict the average weight for all women with that same height.
  5. All of the above are true.

Answer:c

  1. Suppose a researcher examined 100 possible relationships between the different measurement variables in her study, and found five of them to be statistically significant. Would these five statistically significant relationships have been more, less, or equally meaningful if they had been the only five relationships that were examined in her study?

Answer: these five relationships would have been more meaningful if they had been the only five examined. since 5% of all relationships occurring by chance will be found to be significant, and 5 out of 100 is 5%, the results she has now are not very meaningful.

  1. Explain how sample size can affect whether or not a relationship is found to be statistically significant (discuss the very small and very large sample cases).

Answer: if the sample size is very small, a relationship that exists in the population may go undetected (not statistically significant). If the sample size is very large, a relationship that is not very strong in the population may be detected (statistically significant).

  1. Most researchers are willing to declare that a relationship is statistically significant if the chances of observing the relationship in the sample when actually nothing is going in the population are less than what percent?
  2. 5%
  3. 50%
  4. 95%
  5. None of the above

Answer:a

  1. A relationship is considered to be statistically significant if that relationship is stronger than what percent of the relationships we would expect to see just by chance?
  2. 5%
  3. 95%
  4. 50%
  5. None of the above

Answer:b

  1. Which of the following statements is true?
  2. If a relationship is found to be statistically significant, there is a strong relationship between the two measurement variables.
  3. A relationship that is not found to be strong can still be statistically significant.
  4. If researchers fail to find a statistically significant relationship, then no relationship exists between the two measurement variables.
  5. None of the above statements are true.

Answer:b

  1. Which of the following is true if a relationship is found to be statistically significant?
  2. Researchers have declared that the relationship found in the sample is not a fluke.
  3. The chances of observing the relationship in the sample when nothing is actually going on in the population are small (less than 5%).
  4. This relationship is stronger than 95% of the relationships we would expect to see just by chance.
  5. All of the above.

Answer:d

  1. To be convincing, an observed relationship must also be statistically ______.

Answer: significant

  1. The ______of the sample can greatly affect whether or not a relationship is found to be statistically ______.

Answer: size, significant

  1. Determine whether or not the following statement could be statistically correct. If not, explain why not. “The correlation between tree diameter and weight of fruit harvested was found to be 2.3.”

Answer: no. correlation must be between -1 and +1.

  1. Determine whether or not the following statement could be statistically correct. If not, explain why not. “We found a strong correlation between gender and political party.”

Answer: no. correlation refers to two measurement variables.

  1. Determine whether or not the following statement could be statistically correct. If not, explain why not. “The correlation between height and weight is +0.8, so the correlation between weight and height must be −0.8.”

Answer: no. correlation is not affected by the ordering of the two measurement variables.

  1. Determine whether or not the following statement could be statistically correct. If not, explain why not. “The correlation between tree diameter and tree height in feet is .69. In yards, this correlation would become .69/3 = .23.”

Answer: no. correlation is not affected by a change in units.

  1. Which of the following describes a strong statistical correlation?
  2. The value of one measurement variable is always equal to the square of the value of another measurement variable.
  3. One measurement variable has a cause and effect relationship with another measurement variable.
  4. Two measurement variables have a strong linear relationship.
  5. All of the above.

Answer:c

  1. Suppose the correlation between two measurement variables is −1. Which of the following statements is not true?
  2. As one of the variables increases, the other decreases.
  3. The data looks the same as when two variables have a deterministic linear relationship.
  4. The correlation between the variables is very weak.
  5. All of the above statements are true.

Answer:c

  1. Which of the following is a correct interpretation of a correlation?
  2. “The correlation is −.85. This means students with lower verbal SAT scores tend to have lower GPAs as well.”
  3. “The correlation between husbands’ and wives’ ages is −.85, so the correlation between wives’ and husbands’ ages is +.85.”
  4. “The correlation is −.85. This means that as the distance of a golf putt goes up, the success rate of making the putt goes down..”
  5. All of the above.

Answer:c

  1. A researcher wants to explore the relationship between cricket chirps and temperature. The following scatterplot shows data collected over a random sample of 8 days. Each day, the temperature was recorded, as well as the number of times a cricket chirped in 15 seconds. According to this scatterplot, what can be said (if anything) about the relationship between cricket chirps and temperature?

  1. There appears to be a strong positive linear relationship.
  2. There appears to be a weak linear relationship because the slope of the line is fairly flat.
  3. There can’t be a relationship; cricket chirps can’t be related to temperature.
  4. None of the above.

Answer:a

  1. The ______between two measurement variables is an indicator of how closely their values fall to a straight line.

Answer: correlation

  1. If there is no linear relationship between two measurement variables, the correlation is ______.

Answer: zero

Narrative: Study time and exam score

Suppose an algebra professor found that the correlation between study time (in hours) and exam score (out of 100) is +.80, and the regression line was found to be y = 20 + 4x. He arrived at this equation through years of collecting data on his students, most of whom reported studying anywhere from 0 to 20 hours for his exams.

  1. {Study time and exam score narrative} Which variable is X and which variable is Y in this situation?

Answer: x=study time (in hours); y=score (out of 100).

  1. {Study time and exam score narrative} What meaning (if any) does the y intercept of 20 have in this situation? Use words that a non-statistics student would be able to understand.

Answer: For students who don’t study at all, their expected score is 20 points.

  1. {Study time and exam score narrative} What meaning (if any) does the slope of 4 have in this situation? Use words that a non-statistics student would be able to understand.

Answer: For every hour increase in study time, there is a 4 point increase in expected exam scores, on average.

  1. {Study time and exam score narrative} In order to get a 100 on this exam, how long should students expect to study (minimum)?

Answer: 20 hours.

  1. {Study time and exam score narrative} For which values of study time does the professor’s regression equation make sense in terms of predicting exam scores?
  2. Between 0 and 20 hours.
  3. Between 0 and 100 hours.
  4. Anything greater than or equal to 0 hours.
  5. It is not possible to predict exam score with study time.

Answer:a

  1. {Study time and exam score narrative} Suppose the professor later found out that his correlation was not +.80, but rather it was +.08. How does this change the predictions he can make about exam scores based on study time?
  2. You have to take the results and divide them by 10, because .80/10 = .08.
  3. It won’t change the predictions because the regression line stays the same.
  4. The predictions should no longer be used because they won’t be very accurate.
  5. Not enough information to tell.

Answer:c

Narrative: Crickets and temperature

A researcher wants to explore the relationship between cricket chirps and temperature. The following scatterplot shows data collected over a random sample of 8 days. Each day, the temperature was recorded, as well as the number of times a cricket chirped in 15 seconds. The correlation was found to be over .90. The least squares line was found to be Temperature (in Fahrenheit) = 40 + 1.0 × (#Chirps in 15 seconds).

  1. {Crickets and temperature narrative} For about what range of cricket chirps can the researcher feel comfortable about making temperature predictions?
  2. 15-40 chirps per 15 seconds
  3. 60-80 degrees
  4. 0-40 chirps per 15 seconds
  5. Any range is acceptable.

Answer:a

  1. {Crickets and temperature narrative} On nights when crickets chirp 20 times in 15 seconds, what do you predict the temperature to be, on average?

Answer: 60 degrees fahrenheit

  1. {Crickets and temperature narrative} On nights when crickets chirp 120 times per minute, what do you predict the temperature to be, on average?

Answer: 70 degrees fahrenheit