Chemistry: The Science in Context (Fifth Edition)
Chemistry: The Science in Context (Fifth Edition)
5th Edition
ISBN: 9780393614046
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster, Stacey Lowery Bretz, Geoffrey Davies
Publisher: W. W. Norton & Company
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Chapter 1, Problem 1.91AP

(a)

Interpretation Introduction

Interpretation: The data for the distribution if trail mix is given. The mean and standard deviation in the percentage of peanut and that of raisins in the four samples is to be calculated. Also the 90% confidence interval of the percentages is to be checked to include the target composition of peanuts and raisins.

Concept introduction: The standard deviation is calculated as,

Standarddeviation=(xx¯)2Numberofsamples

The 90% confidence interval is calculated by the formula,

Mean±1.645×StandarddeviationNumberofsamples

To determine: The mean and standard deviation in the percentage of peanut and that of raisins in the four samples.

(a)

Expert Solution
Check Mark

Answer to Problem 1.91AP

Solution

The value of mean and standard deviation of percentage of peanut is 62.81_ and 3.61_ , respectively.

The value of mean and standard deviation of percentage of peanut is 37.19_ and 3.61_ , respectively.

Explanation of Solution

Explanation

Given

The data for the amount of peanuts and raisins are given as,

DayPeanutsRaisins15032115626214834315230

The total content of the peanuts and raisins on day 1 is 50+32=82 .

Therefore, the percentage of the peanuts on day one is 5082×100=61% and that of raisins is 10061=39% .

The total content of the peanuts and raisins on day 2 is 56+26=82 .

Therefore, the percentage of the peanuts on day one is 5682×100=68.3% and that of raisins is 10068.3=31.7% .

The total content of the peanuts and raisins on day 3 is 48+34=82 .

Therefore, the percentage of the peanuts on day one is 4882×100=58.54% and that of raisins is 10058.54=41.46% .

The total content of the peanuts and raisins on day 1 is 52+30=82 .

Therefore, the percentage of the peanuts on day one is 5282×100=63.4% and that of raisins is 10063.4=36.6% .

Therefore, the table for the calculation of the standard deviation for peanut is,

Dayx(%Peanut)xx¯(xx¯)21611.813.2761268.35.4930.1401358.544.2718.2329463.40.590.3481Mean(x¯)62.81

The mean of the percentage of peanut is given by the formula,

Mean=Sumofallthepercentagestotalnumberofsamples

Substitute the values of all the percentages and the number of samples of peanuts in the above equation.

Mean=61+68.3+58.54+63.44=62.81

The standard deviation is calculated as,

Standarddeviation=(xx¯)2Numberofsamples

Substitute the value of (xx¯)2 and the number of samples in the above equation.

Standarddeviation=3.2761+30.1401+18.2329+0.34814=51.99724=12.9993=3.61

Therefore, the value of mean and standard deviation of percentage of peanut is 62.81_ and 3.61_ , respectively.

The table for the calculation of the standard deviation for raisins is,

Dayx(%Peanut)xx¯(xx¯)21391.813.2761231.75.4930.1401341.464.2718.2329436.60.590.3481Mean(x¯)37.19

The mean of the percentage of raisins is given by the formula,

Mean=Sumofallthepercentagestotalnumberofsamples

Substitute the values of all the percentages and the number of samples of raisins in the above equation.

Mean=39+31.7+41.46+36.64=37.19

The standard deviation is calculated as,

Standarddeviation=(xx¯)2Numberofsamples

Substitute the value of (xx¯)2 and the number of samples in the above equation.

Standarddeviation=3.2761+30.1401+18.2329+0.34814=51.99724=12.9993=3.61

Therefore, the value of mean and standard deviation of percentage of raisins is 37.19_ and 3.61_ , respectively.

(b)

Interpretation Introduction

To determine: If the 90% confidence interval of the percentages is include the target composition of peanuts and raisins.

(b)

Expert Solution
Check Mark

Answer to Problem 1.91AP

Solution

The 90% confidence interval of peanut is 65.78%-59.84%_ and it does not include the target composition of 67% of peanuts.

The 90% confidence interval of raisins is 40.16%-34.22%_ and it does not include the target composition of 33% of raisins.

Explanation of Solution

Explanation

The 90% confidence interval is calculated by the formula,

Mean±1.645×StandarddeviationNumberofsamples (1)

Therefore, 90% confidence interval of peanut is calculated by substituting its value for mean and standard deviation in the above equation.

62.81%±1.645×3.614%=62.81%±2.97%

Therefore, the 90% confidence interval of peanut is 65.78%-59.84%_ and it does not include the target composition of 67% of peanuts.

90% confidence interval of raisins is calculated by substituting its value for mean and standard deviation in the above equation.

37.19%±1.645×3.614%=37.19%±2.97%

Therefore, the 90% confidence interval of raisins is 40.16%-34.22%_ and it does not include the target composition of 33% of raisins.

Conclusion

  1. a. The value of mean and standard deviation of percentage of peanut is 62.81_ and 3.61_ , respectively.

    The value of mean and standard deviation of percentage of peanut is 37.19_ and 3.61_ , respectively.

  2. b. The 90% confidence interval of peanut is 65.78%-59.84%_ and it does not include the target composition of 67% of peanuts.

    The 90% confidence interval of raisins is 40.16%-34.22%_ and it does not include the target composition of 33% of raisins

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Chapter 1 Solutions

Chemistry: The Science in Context (Fifth Edition)

Ch. 1 - Prob. 1.2VPCh. 1 - Prob. 1.3VPCh. 1 - Prob. 1.4VPCh. 1 - Prob. 1.5VPCh. 1 - Prob. 1.6VPCh. 1 - Prob. 1.7VPCh. 1 - Prob. 1.8VPCh. 1 - Prob. 1.9QPCh. 1 - Prob. 1.10QPCh. 1 - Prob. 1.11QPCh. 1 - Prob. 1.12QPCh. 1 - Prob. 1.13QPCh. 1 - Prob. 1.14QPCh. 1 - Prob. 1.15QPCh. 1 - Prob. 1.16QPCh. 1 - Prob. 1.17QPCh. 1 - Prob. 1.18QPCh. 1 - Prob. 1.19QPCh. 1 - Prob. 1.20QPCh. 1 - Prob. 1.21QPCh. 1 - Prob. 1.22QPCh. 1 - Prob. 1.23QPCh. 1 - Prob. 1.24QPCh. 1 - Prob. 1.25QPCh. 1 - Prob. 1.26QPCh. 1 - Prob. 1.27QPCh. 1 - Prob. 1.28QPCh. 1 - Prob. 1.29QPCh. 1 - Prob. 1.30QPCh. 1 - Prob. 1.31QPCh. 1 - Prob. 1.32QPCh. 1 - Prob. 1.33QPCh. 1 - Prob. 1.34QPCh. 1 - Prob. 1.35QPCh. 1 - Prob. 1.36QPCh. 1 - Prob. 1.37QPCh. 1 - Prob. 1.38QPCh. 1 - Prob. 1.39QPCh. 1 - Prob. 1.40QPCh. 1 - Prob. 1.41QPCh. 1 - Prob. 1.42QPCh. 1 - Prob. 1.43QPCh. 1 - Prob. 1.44QPCh. 1 - Prob. 1.45QPCh. 1 - Prob. 1.46QPCh. 1 - Prob. 1.47QPCh. 1 - Prob. 1.48QPCh. 1 - Prob. 1.49QPCh. 1 - Prob. 1.50QPCh. 1 - Prob. 1.51QPCh. 1 - Prob. 1.52QPCh. 1 - Prob. 1.53QPCh. 1 - Prob. 1.54QPCh. 1 - Prob. 1.55QPCh. 1 - Prob. 1.56QPCh. 1 - Prob. 1.57QPCh. 1 - Prob. 1.58QPCh. 1 - Prob. 1.59QPCh. 1 - Prob. 1.60QPCh. 1 - Prob. 1.61QPCh. 1 - Prob. 1.62QPCh. 1 - Prob. 1.63QPCh. 1 - Prob. 1.64QPCh. 1 - Prob. 1.65QPCh. 1 - Prob. 1.66QPCh. 1 - Prob. 1.67QPCh. 1 - Prob. 1.68QPCh. 1 - Prob. 1.69QPCh. 1 - Prob. 1.70QPCh. 1 - Prob. 1.71QPCh. 1 - Prob. 1.72QPCh. 1 - Prob. 1.73QPCh. 1 - Prob. 1.74QPCh. 1 - Prob. 1.75QPCh. 1 - Prob. 1.76QPCh. 1 - Prob. 1.77QPCh. 1 - Prob. 1.78QPCh. 1 - Prob. 1.79QPCh. 1 - Prob. 1.80QPCh. 1 - Prob. 1.81QPCh. 1 - Prob. 1.82QPCh. 1 - Prob. 1.83QPCh. 1 - Prob. 1.84QPCh. 1 - Prob. 1.85QPCh. 1 - Prob. 1.86QPCh. 1 - Prob. 1.87QPCh. 1 - Prob. 1.88QPCh. 1 - Prob. 1.89APCh. 1 - Prob. 1.90APCh. 1 - Prob. 1.91APCh. 1 - Prob. 1.92APCh. 1 - Prob. 1.93APCh. 1 - Prob. 1.94APCh. 1 - Prob. 1.95APCh. 1 - Prob. 1.96APCh. 1 - Prob. 1.97APCh. 1 - Prob. 1.98AP
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