The desired percentage of Sio, 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 ample is normally distributed witha = 0.32 and that x = 5.23. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. Ο H 5.5 Hgiµ 2 5.5 Ο Η,:μ5.5 Hi µ < 5.5 • Ho: H = 5.5 Hgiµ = 5.5 O Hoi H = 5.5 Hi# > 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.) P-value = State the conclusion in the problem context. O 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 sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.
The desired percentage of Sio, 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 ample is normally distributed witha = 0.32 and that x = 5.23. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. Ο H 5.5 Hgiµ 2 5.5 Ο Η,:μ5.5 Hi µ < 5.5 • Ho: H = 5.5 Hgiµ = 5.5 O Hoi H = 5.5 Hi# > 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.) P-value = State the conclusion in the problem context. O 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 sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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Transcribed Image Text:The desired percentage of Sio, 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 Sio, in a
sample is normally distributed with o = 0.32 and that x = 5.23. (Use a = 0.05.)
(a) Does this indicate conclusively that the true average percentage differs from 5.5?
State the appropriate null and alternative hypotheses.
Ho: u = 5.5
Hg: µ 2 5.5
Ho: H
= 5.5
HaiH< 5.5
Ο H, μ 5.5
H: µ # 5.5
Ο H: μ- 5.5
Hai u > 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 not sufficient evidence to conclude that the true average percentage differs from the desired percentage.
O 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 not sufficient evidence to conclude that the true average percentage differs from the desired percentage.
Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.
(b) If the true average percentage is u = 5.6 and a level a = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H? (Round your answer to four decimal places.)
(c) What value of n is required to satisfy a = 0.01 and B(5.6) = 0.01? (Round your answer up to the next whole number.)
n =
samples
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