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Statistical Inference: Confidence Intervals and Hypothesis Testing - Assignment 8, Exercises of Statistics

National University of Modern Languages (NUML)Statistics

Statistics and Probability - STA301 Fall 2017 Assignment 08 Solution.doc

Typology: Exercises

2016/2017

Uploaded on 01/05/2022

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www.vutube.edu.pk
Assignment.8 fall 2007
Question 1 15 Marks
a) The masses, in grams, of thirteen ball bearings taken at random from a batch
are
21.4,23.1,25.9,24.7,23.4,24.5,25.0,22.5,26.9,26.4,25.8,23.2,21.9
Calculate 95% Confidence interval for the mean mass of the population,
supposed normal, from which these masses were drawn(s=1.77)
Solution:
The 95% confidence interval for the mean mass of the population mean is given by:
X
21.4
23.1
25.9
24.7
23.4
24.5
25.0
22.5
26.9
26.4
25.8
23.2
21.9
=314.7
Course Sta301
Student ID / Login ID.
Name.
PVC Name /Code
Due Date.
Total marks. 30
pf3
pf4

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Assignment.8 fall 2007

Question 1 15 Marks a) The masses, in grams, of thirteen ball bearings taken at random from a batch are 21.4,23.1,25.9,24.7,23.4,24.5,25.0,22.5,26.9,26.4,25.8,23.2,21. Calculate 95% Confidence interval for the mean mass of the population, supposed normal, from which these masses were drawn(s=1.77) Solution: The 95% confidence interval for the mean mass of the population mean is given by: X

=314.

Course Sta

Student ID / Login ID.

Name.

PVC Name /Code

Due Date.

Total marks. 30

Now, b) Ten oil tins are taken at random from an automatic filling machine. The mean weight of the tins is 15.8kg and the standard deviation is 0.50kg.Does the sample mean differ significantly from the intended weight of 16kg? Solution: : μ = 16 : μ 16 Level of significance: α = 5 % = 0.

Now by using the area table of χ^2 , we get And And by substituting the values, we get Sol: b) Hypothesis: H0: σ^2 =1. H1: σ^2 1. Level of significance: α =0. Test Statistics: Critical Region: Computations: =17. Conclusion Since our calculated value of χ^2 is greater than the table value, so we reject the null hypothesis at 5% level of significance.