Basic Computation: Testing µ, σ Unknown A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-tailed test of the claim that the population mean is 9.2. (a) Cheek Requirements Is it appropriate to use a Student's t distribution? Explain. How many degrees of freedom do we use? (b) What are the hypotheses? (c) Compute the t value of the sample test statistic. (d) Estimate the P -value for the test. (e) Do we reject or fail to reject H o ? (f) Interpret the results.

Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
Publisher: Cengage Learning
ISBN: 9781337558075

Chapter
Section

Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
Publisher: Cengage Learning
ISBN: 9781337558075
Chapter 9.2, Problem 10P
Textbook Problem
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Basic Computation: Testing µ, σ Unknown A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-tailed test of the claim that the population mean is 9.2.(a) Cheek Requirements Is it appropriate to use a Student's t distribution? Explain. How many degrees of freedom do we use?(b) What are the hypotheses?(c) Compute the t value of the sample test statistic.(d) Estimate the P-value for the test.(e) Do we reject or fail to reject H o ?(f) Interpret the results.

(a)

To determine

Whether we should use student’s t-distribution or not and compute the degrees of freedom.

Explanation of Solution

Since, the value of the parameter σ is not known and the sample size is relatively large. The distribution is mound-shaped and symmetrical. Hence, it is appropriate to use student’s t-distribution.

n

(b)

To determine

The null hypothesis and alternate hypothesis.

(c)

To determine

To find: The test statistic t.

(d)

To determine

To find: The P-value of the test statistic.

(e)

To determine

Whether we reject or fail to reject the null hypothesis for a 1% level of significance.

(f)

To determine

Interpretation for the result.

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