Describe in detail, with sketches as appropriate, the requirements for a setup of a mechanical experiment that allows to measure the weight of individual atoms. Provide details of a sensor (eg. scale, mass), the sensor actuation and the sensor read-out (eg. experimental noise, physical principle). How do you prove that the measured atomic mass stems specifically from the atoms you analyse? (Consider environmental sources of measurement noise)

This question featured in an Oscillations section of a past exam paper. Any help greatly appreciated! Thanks.

In an experiment to test the effectiveness of a new sleeping aid, a sample of 12 patients took the new drug, and a sample of 15 patients took a commonly used drug. Of the patients taking the new drug, the average time to fall asleep was 28.6 minutes with a sample standard deviation of 5.2 minutes, and for the patients taking the commonly used drug the average time was 30.7 minutes with a sample standard deviation of 4.1 minutes. Can you conclude that the mean time to sleep is less for the new drug? Assume that population standard deviations are the same. Take ? = 0.01.

a. Use P-value method to test the hypothesis.  

b. Find 99% confidence interval and use it to test the hypothesis.

c. Clearly write your conclusion.

d. If the true mean difference between the sleep times is 2 minutes, what is the probability that we can recognize it.

An experiment is conducted to select a suitable catalyst for the commercial production of a product used in soaps which is called EDA. 10% of catalysts have poor performance, 20% of catalysts have moderate performance, 50% of catalysts have good performance, and 20% of catalysts have excellent performance. Suppose an engineer randomly selects 12 catalysts for testing.

1. Find the probability that 3 of them show poor performance, 4 of them show good performance, and 5 of them show excellent performance,
2.   Find the probability that 3 of them show moderate performance, 1 of them show poor performance, 3 of them show good performance, and 5 of them show excellent performance,

The authors of a paper describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked to perform a simulated driving task while talking on a cell phone. While performing this task, occasional red and green lights flashed on the computer screen. If a green light flashed, subjects were to continue driving, but if a red light flashed, subjects were to brake as quickly as possible. The reaction time (in msec) was recorded. The following summary statistics are based on a graph that appeared in the paper.

n = 47      x = 53   s = 65

a) Construct a 95% confidence interval for μ, the mean time to react to a red light while talking on a cell phone. (Round your answers to three decimal places.)

(_________ , _________)

b) Suppose that the researchers wanted to estimate the mean reaction time to within 7 msec with 95% confidence. Using the sample standard deviation from the study described as a preliminary estimate of the standard deviation of reaction times, compute the required sample size. (Round your answer up to the nearest whole number.)

n = ?

A team of comparative psychologists are interested in the maternal behavior or rats. In an experiment, 10, 20, and 25 day-old rat pups were separated from their mothers. They then recorded the time (in seconds) required for the mother rats to retrieve the pups. The psychologists were interest in whether retrieval time varies with age. The data are given below. What can be concluded with an α of 0.05?

Make an interpretation based on the results.

At least one of the rat pup ages differed on the mother retrieval time.None of the rat pup ages differed on the mother retrieval time.    

e) Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference =  ; significant:  ---Select--- Yes No
1 vs. 2: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 2: test statistic =  ; significant:  ---Select--- Yes No
1 vs. 3: test statistic =  ; significant:  ---Select--- Yes No

Design an experiment that tests the effect of body temperature on the aerobic capacity in an animal of your choice. What variables would you measure, and how? Include detail about experimental design and instrumentation, to show your understanding of how data are acquired. Present hypothetical data (in graphical form), which support your predictions. Make sure to label your graphs accurately and precisely, and use reasonable values (and units) for parameters measured.

An experiment in which 44.00kJ of heat is added to a cube of metal with initial side length 1.00m and temperature 300.K is performed twice, once with a copper cube and once with a lead cube. Fill in the blanks with "<", ">", "=", "N/A". Select N/A only if a comparison is not possible.

The copper cube's initial volume is  the lead cube's.
The copper cube's initial temperature is  the lead cube's.
The copper cube's final temperature is  the lead cube's.
The copper cube's final volume is  the lead cube's.
The copper cube's final mass is  the lead cube's.
The copper cube's final internal energy is  the lead cube's.

The photogates in the experiment are used to determine the speed of the gliders passing through. The photogates measure the time it takes for the photogate beam to go from being unblocked to blocked to unblocked again. You tell the photogate how long your glider is, and the speed is then calculated.

Given the description of what the photogates do, how will you determine the velocity of the glider?

An experiment was carried out to study the effect of the percentage of ammonium​ (Factor A) and the stir rate​ (Factor B) on the density of the powder produced. The results are in the accompanying table. Complete parts​ (a) through​ (e).

At the 0.01 level of​ significance is there an interaction between the percentage of ammonium and the stir​ rate?

-   Stir_Rate   -
Percent_of_Ammonium   100   150
2%   10.83   8.49
2%   14.64   6.84
2%   18.46   9.05
2%   15.86   9.54
30%   12.29   12.97

30%   15.66   15.62

30%   18.26   15.62
30%   15.77   13.81

A.) Determine the value of the test statistic.

FSTAT=

​(Round to two decimal places as​ needed.)

PValue=

B.) at the .01 level of significance, is there an effect due to the percentage of ammonium?

FSTAT=

PValue=