Q. 9.108 In each of Exercises 9.107-9.112... [FREE SOLUTION]

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Chapter 8: Q. 9.108 (page 389)

In each of Exercises 9.107-9.112, we have provided a sample mean, sample standard deviation, and sample size. In each case, use the one-mean t-test to perform the required hypothesis test at the 5% significance level.
$\overset{炉}{x} = 21, s = 4, n = 32, H_{0} : 渭 = 22, H_{a} : 渭 < 22$

Short Answer

Expert verified

Since $0.05 < P = 0.084 < 0.10$ , the evidence against null hypothesis is moderate

Step by step solution

Step 1. Given information is:

$\overset{炉}{x} = 21, s = 4, n = 32, H_{0} : 渭 = 22, H_{a} : 渭 < 22$

Step 2. Calculating P-value

$Test static, t = \frac{\overset{炉}{x} - 渭_{0}}{\frac{s}{\sqrt{n}}} . . . (*) Under the assumption that H_{0} is true, t follows t distribution with df = 32 - 1 = 31 Observed value of test static, t_{0} = \frac{21 - 22}{\frac{4}{\sqrt{32}}} = - 1.414 Since the given hypothesis is a left tailed test, P value is given by : P - value = P (t 鈮� t_{0}), where t ~ t_{31} = P (t 鈮� - 1.414) = 0.084$

Step 3. Calculating P using MINITAB

$The probability, P (t 鈮� - 1.414) is calculated using MINITAB in the follwing way : Step 1 : Press the Calc menu; Highlight the' Probability Distributions' . Step 2 : Press t . . .; Step 3 : Tick Cumulative Probability and enter the df Degrees of freedom : 31 Step 4 : Tick Input constant and enter the value - 1.414 Input constant : - 1.414 Step 5 : Press Ok Now, P = 0.084 > 伪 = 0.05 Therefore, at 5 % level of significance we reject the null hypothesis, H_{0} : 渭 = 22$

Step 4. Result

$Since 0.05 < P = 0.084 < 0.10, the evidence against null hypothesis is moderate$

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91影视

In each of Exercises 9.107-9.112, we have provided a sample mean, sample standard deviation, and sample size. In each case, use the one-mean t-test to perform the required hypothesis test at the 5% significance level.
$\overset{炉}{x} = 21, s = 4, n = 32, H_{0} : 渭 = 22, H_{a} : 渭 < 22$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Calculating P-value

Step 3. Calculating P using MINITAB

Step 4. Result

One App. One Place for Learning.

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91影视

In each of Exercises 9.107-9.112, we have provided a sample mean, sample standard deviation, and sample size. In each case, use the one-mean t-test to perform the required hypothesis test at the 5% significance level.x炉=21,s=4,n=32,H0:渭=22,Ha:渭<22

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Calculating P-value

Step 3. Calculating P using MINITAB

Step 4. Result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Discrete Mathematics

Mechanics Maths

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

In each of Exercises 9.107-9.112, we have provided a sample mean, sample standard deviation, and sample size. In each case, use the one-mean t-test to perform the required hypothesis test at the 5% significance level.
$\overset{炉}{x} = 21, s = 4, n = 32, H_{0} : 渭 = 22, H_{a} : 渭 < 22$