The following data shows the strength(in Pascal) of material A and B A : 198 199 199 200 202 203 204 206 B : 197 198 200 200 200 202 204 The strength of these materials follow normal distribution. i) Construct a 95% confidence interval for the standard deviation of the strength for material A. ii) Test the mean strength of material A is more than 200 Pascal at significance level alpha = 0.05. iii) Construct a 95% confidence interval for the difference of mean strength of material A and B if the variances are the same.

The following data shows the strength(in Pascal) of material A and B A : 198 199 199 200 202 203 204 206 B : 197 198 200 200 200 202 204 The strength of these materials follow normal distribution. i) Construct a 95% confidence interval for the standard deviation of the strength for material A. ii) Test the mean strength of material A is more than 200 Pascal at significance level alpha = 0.05. iii) Construct a 95% confidence interval for the difference of mean strength of material A and B if the variances are the same.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Question

The following data shows the strength(in Pascal) of material A and B
A : 198 199 199 200 202 203 204 206
B : 197 198 200 200 200 202 204
The strength of these materials follow normal distribution.
i) Construct a 95% confidence interval for the standard deviation of the strength for
material A.
ii) Test the mean strength of material A is more than 200 Pascal at significance level
alpha = 0.05.
iii) Construct a 95% confidence interval for the difference of mean strength of material A
and B if the variances are the same.
iv) Based on the results in Question (iii) test the mean strength of material A and B are the
same at significance level
alpha = 0.05.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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