Could someone please just check my answers for this? I want to make sure I did these right.
1. A student reported the mass of ten glass beads as 2.507 +/- 0.015 g. What should the student report as the mass of one bead? Explain your answer.
A: The student should report the mass of one bead as anything between 2.492 and 2.522. This is true because anything between those numbers would fall in between the range of what the student reported as the mass of the glass beads.
2. A student reported the density of glass beads as 2.05 +/- 0.34 gmL^-1. What should the student report as the density of one glass bead? Explain your answer.
A: The student should report the density of one glass bead as anything between 1.71 and 2.39. This is true because anything between those numbers would fall in between the range of what the student reported as the dnsity of the glass beads.
3. A student measured the mass of ten glass beads five times instead of using five sets of ten randomly selected glass beads. Would you expect that the confidence interval for the mean of the mass measurements would be zero?
I wouldn't expect the confidence interval for the mean of the mass measurements to be zero but rather much higher. The same set of beads would yield the same, or very close to the same, confidence interval and probability that the mean of the mass measurements would be close.
4. A student noticed that the average diameter of the glass beads used for the mass measurements was significantly smaller than those used for the volume measurements. How would experimental determination of the density of glass be affected? Is this a systematic or random error?
Experimental determination of the density of the glass would be affected because the experimental value would be greater than the accepted value. There would be big percent difference. This is a systematic error because an error was made in measurement. It influenced the accuracy of the result.
5. Which of the following terms has the greater effect on random error, p(d): the precision of the mass measurements, indicated by [p(m)/(mean)m]^2; or the precision of the volume measurements, indicated by [p(V)/(mean)V]^2? How might you revise the experimental procedure to reduce this effect?
The precision of the volume measurements has the greater effect on random error. This is because the mass of the beads would all be close to the same, but the volume is harder to calculate due to irreproducibility of an instrument and imprecision among multiple readings. I might revise the experimental procedure to reduce this effect by doing multiple measures of the same construct and making sure data is collected correctly.
1. A student reported the mass of ten glass beads as 2.507 +/- 0.015 g. What should the student report as the mass of one bead? Explain your answer.
A: The student should report the mass of one bead as anything between 2.492 and 2.522. This is true because anything between those numbers would fall in between the range of what the student reported as the mass of the glass beads.
Nope. You have to divide the mass of ten beads by ten to get the mass of one
2. A student reported the density of glass beads as 2.05 +/- 0.34 gmL^-1. What should the student report as the density of one glass bead? Explain your answer.
A: The student should report the density of one glass bead as anything between 1.71 and 2.39. This is true because anything between those numbers would fall in between the range of what the student reported as the dnsity of the glass beads.
Nope. You are missing the point. Density does not change with the number of beads. The density reported should be the same as given
3. A student measured the mass of ten glass beads five times instead of using five sets of ten randomly selected glass beads. Would you expect that the confidence interval for the mean of the mass measurements would be zero?
I wouldn't expect the confidence interval for the mean of the mass measurements to be zero but rather much higher. The same set of beads would yield the same, or very close to the same, confidence interval and probability that the mean of the mass measurements would be close.
Nope. If you take the same reading five times, the confidence interval is zero. Meaningless measurements when it comes to the deviation of the individual beads
4. A student noticed that the average diameter of the glass beads used for the mass measurements was significantly smaller than those used for the volume measurements. How would experimental determination of the density of glass be affected? Is this a systematic or random error?
Experimental determination of the density of the glass would be affected because the experimental value would be greater than the accepted value. There would be big percent difference. This is a systematic error because an error was made in measurement. It influenced the accuracy of the result.
Nope. If the measured mass is smaller, and the measured volume is larger, the calculated density will be smaller. What you wrote is gibberish
5. Which of the following terms has the greater effect on random error, p(d): the precision of the mass measurements, indicated by [p(m)/(mean)m]^2; or the precision of the volume measurements, indicated by [p(V)/(mean)V]^2? How might you revise the experimental procedure to reduce this effect?
The precision of the volume measurements has the greater effect on random error. This is because the mass of the beads would all be close to the same, but the volume is harder to calculate due to irreproducibility of an instrument and imprecision among multiple readings. I might revise the experimental procedure to reduce this effect by doing multiple measures of the same construct and making sure data is collected correctly.
Nope. I assume you did not measure volume, but measured diameter. That is the measurement which had precision. Now to get volume, you probably cubed diameter, and that greatly magnifies error
1. A student should report the mass of one bead as the mass of ten beads (2.507 g) divided by ten, which is 0.2507 g.
2. The student should report the density of one glass bead as the density of the glass beads (2.05 gmL^-1) since density does not change with the number of beads.
3. If the student measured the mass of the same ten beads five times, the confidence interval for the mean of the mass measurements would be zero because the measurements would be identical. This does not provide any information about the individual beads.
4. The experimental determination of the density of glass would be affected if the average diameter of the glass beads used for mass measurements was smaller than those used for volume measurements. This is likely a systematic error because there was a consistent difference in the measurements. The calculated density would be smaller because the measured volume would be larger and the measured mass would be smaller.
5. The precision of the volume measurements has a greater effect on random error because any error in measuring the diameter is cubed when calculating volume. To reduce this effect, the experimental procedure could be revised by improving the precision of measuring the diameter, using more precise instruments, and taking multiple readings to account for any variability.
1. The student should report the mass of one bead as the mass of ten beads divided by ten. In this case, 2.507 g divided by 10, which gives a value of 0.2507 g for the mass of one bead.
2. The student should report the density of one glass bead as the density of the glass beads reported. In this case, 2.05 gmL^-1.
3. If the student measured the mass of the same set of beads five times, the confidence interval for the mean of the mass measurements would be zero because there is no variability in the measurements. The same set of beads will yield the same average every time, resulting in a confidence interval of zero.
4. If the average diameter of the glass beads used for mass measurements is significantly smaller than those used for volume measurements, it would affect the experimental determination of the density of glass. The calculated density would be smaller than the actual value because the smaller diameter would result in a smaller volume. This is a systematic error, as it was consistently observed throughout the measurements and has influenced the accuracy of the result.
5. The precision of the mass measurements has a greater effect on random error, p(d), compared to the precision of the volume measurements. This is because the mass measurements have a squared term in the calculation formula, [(p(m)/(mean(m))]^2, which amplifies the effect of any variation in the mass measurements. To reduce this effect, the experimental procedure could be revised by improving the precision of the mass measurements through the use of more accurate and consistent weighing instruments and ensuring proper technique and calibration.
1. The student should report the mass of one bead as the mean mass of the ten beads divided by ten. In this case, the mean mass is 2.507 g, so the mass of one bead would be 2.507 g / 10 = 0.2507 g.
2. The student should report the density of one glass bead as the same as the density of the glass beads given, which is 2.05 gmL^-1. The density of a substance does not change based on the number of particles considered.
3. If the student measured the mass of the same set of ten glass beads five times, the confidence interval for the mean of the mass measurements would likely be very small or even zero. This is because the repeated measurements on the same set of beads would not provide additional information and would not account for the natural variation that would occur with different sets of beads. Therefore, the confidence interval would not accurately represent the range of values for the mass of glass beads.
4. If the average diameter of the glass beads used for the mass measurements was significantly smaller than those used for the volume measurements, the experimental determination of the density of glass would be affected. This is because the volume of a sphere is calculated using the cube of its diameter. If the diameter is smaller, the calculated volume will be smaller, resulting in a higher density value. This is a systematic error because it consistently affects the measurements in the same direction, leading to a bias in the results.
5. The precision of the volume measurements has a greater effect on random error (p(d)) compared to the precision of the mass measurements. This is because volume is calculated from the cube of the diameter, which magnifies any errors in the diameter measurements. To reduce this effect, one could improve the precision of the diameter measurements by using more accurate instruments or techniques. Additionally, taking multiple measurements and calculating the average diameter would help reduce the effect of random errors.