Answered: (b) If the true average percentage is…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

The desired percentage of SiO₂ in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO₂ in a sample is normally distributed with ? = 0.32 and that x = 5.21. (Use ? = 0.05.)

(a) Does this indicate conclusively that the true average percentage differs from 5.5?
State the appropriate null and alternative hypotheses.

H₀: ? = 5.5
H_a: ? ≠ 5.5H₀: ? = 5.5
H_a: ? ≥ 5.5 H₀: ? = 5.5
H_a: ? < 5.5H₀: ? = 5.5
H_a: ? > 5.5

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

State the conclusion in the problem context.

Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage.

(b) If the true average percentage is

? = 5.6

and a level ? = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H₀? (Round your answer to four decimal places.)

(c) What value of n is required to satisfy ? = 0.01 and ?(5.6) = 0.01? (Round your answer up to the next whole number.)
n = samples

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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