Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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![OMOGOLO NALEDI N SETLALEKGaasi
NALEDI SETLALEIGOS!
202100532
MATH TEST 1 [v
Question 1
(a) 10
75
Question B4
(a) According to Mendelian genetic model, the offspring of a certain cross of bearded iris plants
should be coloured pink, blue or red with probabilities
Suppose an experiment yields 58, 44 and 42 in each category.
(i) Draw a table and showing the model yields and experiment yields.
(ii) Evaluate the X and the critical value of the test where we use chi-square test at
5% significant level.
9
3
16 16
16
and , respectively.
[3]
[2]
[5]
[3]
V(iii) State the decision rule for the test, showing clearly the acceptance and the rejection region
of the test.
(iv) Give a conclusion on whether the experiment support the theory or not?
(b) The following measurements were recorded for the drying time, in hours, of a certain brand
of latex paint:
1 2 3 4 5 6 7 8 9 10 11 12 1
3.4, 2.5, 4.8, 2.9, 3.6, 2.8, 4.0, 5.2, 3.0, 4.8, 3.0, 4.6, 5.1
Assuming that the measurements represent a random sample from a normal population.
(i) Find a 95% confidence interval for the mean drying time for the next trial of the paint. [10]
(ii) If a paint has a drying time of 2.3 hours, does it belong to this brand of latex paint?
[2]](https://content.bartleby.com/qna-images/question/2006393e-c97e-4081-8173-0190425f3dd9/ebad440b-0de5-4d20-8566-9b5f157535af/2wpo26d_processed.jpeg)
Transcribed Image Text:OMOGOLO NALEDI N SETLALEKGaasi
NALEDI SETLALEIGOS!
202100532
MATH TEST 1 [v
Question 1
(a) 10
75
Question B4
(a) According to Mendelian genetic model, the offspring of a certain cross of bearded iris plants
should be coloured pink, blue or red with probabilities
Suppose an experiment yields 58, 44 and 42 in each category.
(i) Draw a table and showing the model yields and experiment yields.
(ii) Evaluate the X and the critical value of the test where we use chi-square test at
5% significant level.
9
3
16 16
16
and , respectively.
[3]
[2]
[5]
[3]
V(iii) State the decision rule for the test, showing clearly the acceptance and the rejection region
of the test.
(iv) Give a conclusion on whether the experiment support the theory or not?
(b) The following measurements were recorded for the drying time, in hours, of a certain brand
of latex paint:
1 2 3 4 5 6 7 8 9 10 11 12 1
3.4, 2.5, 4.8, 2.9, 3.6, 2.8, 4.0, 5.2, 3.0, 4.8, 3.0, 4.6, 5.1
Assuming that the measurements represent a random sample from a normal population.
(i) Find a 95% confidence interval for the mean drying time for the next trial of the paint. [10]
(ii) If a paint has a drying time of 2.3 hours, does it belong to this brand of latex paint?
[2]
![Question B3
OMOGOLO NALEDI N SETALEGOSI
102100532
NALEDI SETLALEKGOS!
202100532
MAT 271
(a) The breaking strength X of a certain rivet used in a machine engine has a mean 4000 psi and
standard deviation 80 psi. A random sample of 64 rivets is taken. Consider the distribution of
X, sample mean breaking strength.
i) State the Central Limit Theorem.
[2]
[4]
ii) What is the probability that the sample mean falls between 3985 psi and 4025 psi?
iii) What sample size n, would be necessary to have P(3992<X<4008)=0.95? [4]
(b) The pressure Y of a gas corresponding to various volumes X is recorded, and the data is
tabulated follows:
Volume X(cm³)
Pressure Y(kg/cm³)
40 50 55 60 80 90
64.7 45.2 40.1 37.6 12.6 7.5
i) Using the model x =ay, +b+&,,i=1,2,...,6 find the least square estimate for a
and b. Hence write the regression line x=ây+b.
[8]
ii) Determine the volume, if the pressure is 5.2kg/cm³
[2]
iii) Determine the volume, if the pressure is 76.4kg/cm³
[2]
iv) Compute and interpret the sample correlation coefficient r of the data.
[3]](https://content.bartleby.com/qna-images/question/2006393e-c97e-4081-8173-0190425f3dd9/ebad440b-0de5-4d20-8566-9b5f157535af/709v45k_processed.jpeg)
Transcribed Image Text:Question B3
OMOGOLO NALEDI N SETALEGOSI
102100532
NALEDI SETLALEKGOS!
202100532
MAT 271
(a) The breaking strength X of a certain rivet used in a machine engine has a mean 4000 psi and
standard deviation 80 psi. A random sample of 64 rivets is taken. Consider the distribution of
X, sample mean breaking strength.
i) State the Central Limit Theorem.
[2]
[4]
ii) What is the probability that the sample mean falls between 3985 psi and 4025 psi?
iii) What sample size n, would be necessary to have P(3992<X<4008)=0.95? [4]
(b) The pressure Y of a gas corresponding to various volumes X is recorded, and the data is
tabulated follows:
Volume X(cm³)
Pressure Y(kg/cm³)
40 50 55 60 80 90
64.7 45.2 40.1 37.6 12.6 7.5
i) Using the model x =ay, +b+&,,i=1,2,...,6 find the least square estimate for a
and b. Hence write the regression line x=ây+b.
[8]
ii) Determine the volume, if the pressure is 5.2kg/cm³
[2]
iii) Determine the volume, if the pressure is 76.4kg/cm³
[2]
iv) Compute and interpret the sample correlation coefficient r of the data.
[3]
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