Given the following hypotheses: H0: μ = 540 H1: μ ≠ 540 A random sample of 10 observations is selected from a normal population. The sample mean was 550 and the sample standard deviation was 6. Using the 0.10 significance level: State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.) Compute the value of the test statistic. (Round your answer to 3 decimal places.)
ANSWER:
Given that,
Sample size = n = 10
Sample mean = = 550
Standard deviation = s = 6
a) Null and alternative hypothesis is
H0: μ = 540
H1: μ ≠ 540
Test statistic is
=550-540/(6/3.1623)
= 10/1.897
=5.271
Degrees of freedom = n - 1 = 10 - 1 = 9
Critical value = 1.833 ( Using t table)
Decision Rule : Test statistic > critical value we reject null hypothesis.
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