Given the following hypothesis: H_0: mu lessthanorequalto 12 H_1: mu > 12 For a

Question

Given the following hypothesis: H_0: mu lessthanorequalto 12 H_1: mu > 12 For a random sample of 10 observations, the sample mean was 15 and the sample standard deviation 5.00. Using the 0.010 significance level: (a) State the decision rule. (Round your answer to 3 decimal places.) Reject H_0 if t > 2.821 (b) Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Value of the test statistic 1.89 (c)What is your decision regarding the null hypothesis? evidence to conclude that the population mean is greater than 12.

Explanation / Answer

Question a)

We need to find one-tailed critical t value for 9 degrees of freedom at 1% level of significance.

tc = 2.821

Answer: Reject Ho if t > 2.821

Question b)

t = ( x bar – Mew)/(s/sqrt(n))

= (15-12)/(5/sqrt(10))

= 1.897

Answer: Value of the test statistics 1.897

Question c)

Here the test statistics is greater than the critical value (1.897>2.821); we reject the null hypothesis.

Reject Ho. There is sufficient evidence to conclude that the population mean is greater than 12.

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