Question

In: Statistics and Probability

Many studies have been conducted to determine the concentration of CO (carbon monoxide) near freeways with...

Many studies have been conducted to determine the concentration of CO (carbon monoxide) near freeways with various conditions of traffic flow. The basic technique involves measuring CO concentrattions with a spectrophotometer. These machines are quite delicate and have to be calibrated every day. If the machine reads close to 70 ppm on the span gas, it’s ready for use; if not, it has to be adjusted.
Each data set below represents some readings on span gas. Assume the Gaussian model, with errors following the normal curve. In each case, make a t-test to see whether the instrument is properly calibrated or not.
a) 71, 68, 79
b) 71, 68, 79, 84, 78, 85, 69
c) 71
d) 71, 84

Solutions

Expert Solution

To know, if the calibration is proper or not, we will run a 1 sample-t test

Null hypothesis: There is no significant difference between the mean reading of the machine and 70 ppm

Alternate hypothesis: There is a significant difference between the mean reading of the machine and 70 ppm

Readings
71
68
79
71
68
79
84
78
85
69
71
71
84
sample size (n) 13
Mean (µ) 75.2
Standard deviation (σ)(s) 6.5
df (n-1) 12

Assuming confidence level of 95%

with CI of 95% and df of 12, t value as per below table is 1.7832

We get below values

One-Sample T: Readings

Descriptive Statistics

N Mean StDev SE Mean 95% CI for μ
13 75.23 6.46 1.79 (71.33, 79.13)

μ: mean of Readings

Test

Null hypothesis H₀: μ = 70
Alternative hypothesis H₁: μ ≠ 70
T-Value P-Value
2.92 0.013

Since p-value is less than the level of significance, we reject the null hypothesis and conclude that there is a significant difference between the mean reading of the machine and 70 ppm

Hence the machine needs calibration


Related Solutions

Many research studies have been conducted to examine how different organizations are on implementing knowledge management...
Many research studies have been conducted to examine how different organizations are on implementing knowledge management process. For example, studies have proved that larger firms have more resources to utilize, and so they have taken more efforts to implement knowledge management process. The Journal of Business Research (Aug. 2014) published a study* discussing the relationship between knowledge management process and organizational performance. The table below shows the percentage of different size of firms participated in the study. These firms have...
If the concentration (solubility) of carbon monoxide in water is 0.27 M and the Henry's Law...
If the concentration (solubility) of carbon monoxide in water is 0.27 M and the Henry's Law constant for carbon monoxide is 9.5 x 10-4 M/atm, what is the partial pressure of the gas above the solution? A solution is prepared by adding 3.65 x 10-3 g of sodium carbonate to 575 g of water. Find ppb and molality
the concentration of carbon monoxide in an urban apartment is 48 micrograms/m^3. What mass of carbon...
the concentration of carbon monoxide in an urban apartment is 48 micrograms/m^3. What mass of carbon monoxide in grams is present in a room measuring 10.5 x 13.5 x 22.5
The relationship between the amount of remaining carbon monoxide (CO) in an individual’s lungs and the...
The relationship between the amount of remaining carbon monoxide (CO) in an individual’s lungs and the time since that person last smoked a cigarette can be summarized using a linear regression approach. (a) Write down a simple linear regression model and the underlying assumptions. The following summary data was collected from 12 different smokers. x = time since last smoked a cigarette (hours) y = amount of CO in ppm n=12, x=1.88 sxx =25.8, syy =1805 SSE=877.4 Fitted regression line:...
The relationship between the amount of remaining carbon monoxide (CO) in an individual’s lungs and the...
The relationship between the amount of remaining carbon monoxide (CO) in an individual’s lungs and the time since that person last smoked a cigarette can be summarized using a linear regression approach. (a) Write down a simple linear regression model and the underlying assumptions. The following summary data was collected from 12 different smokers. x = time since last smoked a cigarette (hours) y = amount of CO in ppm n=12, x=1.88 sxx =25.8, syy =1805 SSE=877.4 Fitted regression line:...
Consider the decomposition of acetaldehyde (CH3CHO) into methane (CH4) and carbon monoxide (CO).
Consider the decomposition of acetaldehyde (CH3CHO) into methane (CH4) and carbon monoxide (CO).CH3CHO → CH4 + COAn experiment is performed where the concentration of acetaldehyde is measured at various time intervals, resulting in the following data.Time (s)[CH3CHO] (M)0.00.24220.00.16840.00.12960.00.104(a) Using Excel (or similar software), graph the three types of plots outlined below and enter the slope, y-intercept, and R2 for each graph). Use the graph with the best linear fit to determine the order of the reaction with respect to CH3CHO....
The relationship between the amount of remaining carbon monoxide (CO) in an individual’s lungs and the...
The relationship between the amount of remaining carbon monoxide (CO) in an individual’s lungs and the time since that person last smoked a cigarette can be summarized using a linear regression approach. Write down a simple linear regression model and the underlying assumptions. The following summary data was collected from 12 different smokers. x = time since last smoked a cigarette (hours) y = amount of CO in ppm n=12, x=1.88 sxx =25.8, syy =1805 SSE=877.4 Fitted regression line: ?̂...
A 0.020 mol sample of carbon monoxide (CO) is placed in a cylinder fitted with a...
A 0.020 mol sample of carbon monoxide (CO) is placed in a cylinder fitted with a movable frictionless piston. This gaseous sample - initially at volume Vi = 4.00 L - has a pressure of 0.400 atm - identical to the external pressure. This gaseous sample then undergoes a cyclic process. Throughout the cyclic process, the sample is thermostatted at a Kelvin temperature T. The details of this cyclic process: First, a two-step expansion carried out as follows:    The...
The carbon monoxide (CO) level in a manufacturing plant is supposed to be about 50 parts...
The carbon monoxide (CO) level in a manufacturing plant is supposed to be about 50 parts per million (ppm). However there is concern that actual CO levels are higher than the acceptable level.Five CO measurements are taken at various times during the day and reading are given below. 58 63 48 52 68 (a)At 5% level of significance test whether the mean CO level is higher that 60 ppm. (b)Find a 95% confidence interval for the mean CO level.
The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain...
The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it​ best? Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not? TAR NICOTINE CO 6 0.4 5 15 1.0 18 16 1.3 16 13 0.7 18 13 0.8 18 13 0.9 14 16 1.0 17 16...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT