MS 150 Statistics Midterm • Name:

In physical science laboratory six the students measured the distance d in cm a marble of mass m would roll after being released from a ramp at a constant height h. All groups chose to roll the marble multiple times and take the average of the marble distance d.

d (cm)
180
180
190
190
200
200
220
230
230
230
230
230
230
230
240

Marble or sphere on ruler track or table Marble or sphere on a flat surface ruler distance = 0 cm distance d marble roll stop marble start wood block

  1. __________ What level of measurement is the data?
  2. __________ Find the sample size n for the data.
  3. __________ Find the minimum.
  4. __________ Find the maximum.
  5. __________ Find the range.
  6. __________ Find the midrange.
  7. __________ Find the mode.
  8. __________ Find the median.
  9. __________ Find the sample mean x.
  10. 21.31 Freebie: This is the standard deviation sx. If you obtain a different value, then you typed in the wrong data! Calculate the standard deviation sx and check for agreement.
  11. __________ Find the sample coefficient of variation CV.
  12. __________ If this data were to be divided into six classes, what would be the width of a single class?
  13. Determine the frequency and calculate the relative frequency using six classes. Record your results in the table provided.
distance CUL (cm)Frequency (f)Relative Frequency
Sum:
  1. Sketch a frequency histogram chart of the data anywhere it fits, labeling your horizontal axis and vertical axis as appropriate.
  2. ____________________ What is the shape of the distribution?
  3. p(d = 230) = ____________________ What is the probability a marble will roll 230 cm?
  4. ____________________ Use the sample mean x and standard deviation sx calculated above to determine the z-score for a marble that rolled at 173 cm.
  5. ____________________ Is the z-score for 173 cm an ordinary or unusual z-score?
  6. ____________________ Based on the z-score, would a 173 cm roll be considered an outlier?

Part II: Linear regression

Marble distance background rectangle major grid lines axes coordinate labels for the circles below (0.4,18) (1.8,125) (5.6,214) (19.4,318) data points as circles text layers Marble mass versus distance 19 Feb 09 mass (g) dist (cm) y-axis labels 18 48 78 108 138 168 198 228 258 288 318 x-axis labels 0.4 2.3 4.2 6.1 8.0 9.9 11.8 13.7 15.6 17.5 19.4

In physical science laboratory six the students measured the distance d a marble of mass m would roll after being released from a ramp at a constant height h. The following table contains mass m versus average distance d data for four marbles.

Typemass (g)dist (cm)
ball bearing (BB)0.418
small marble1.8125
marble5.6214
shooter19.4318
  1. __________ Calculate the slope of the linear regression for the data.
  2. __________ Calculate the y-intercept of the linear regression for the data.
  3. __________ Use the slope and intercept to predict the distance d that a marble with a mass m of 1.1 g would roll.
  4. __________ Use the slope and intercept to predict the mass m that would produce a distance d of 303 cm.
  5. __________ Does the relationship appear to be linear, non-linear, or random?
  6. __________ Is the correlation positive, negative, or neutral?
  7. __________ Determine the correlation coefficient r.
  8. __________ What is the strength of the correlation: strong, moderate, weak, or none?
  9. __________ Determine the coefficient of determination r².
  10. __________ What percent of the variation in the mass m explains the variation in the distance d?
  11. __________ Does the linear regression line look like a good predictor of distance for masses significantly larger than 20 grams?