Given the following hypothesis: H0 : 11 H1 : > 11 For a random sample of 10 obse

Question

Given the following hypothesis: H0 : 11 H1 : > 11 For a random sample of 10 observations, the sample mean was 12 and the sample standard deviation 5.00. Using the 0.025 significance level: (a) State the decision rule. (Round your answer to 3 decimal places.) Reject H0 if t >____ (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 (c) What is your decision regarding the null hypothesis? ______ (Reject/Do not reject) H0. There is _____(sufficient/insuffiecient)evidence to conclude that the population mean is greater than 11.

Explanation / Answer

Solution:

Given x = 12, = 11, s = 5, n = 10
a) Decision rule: Reject null or H0 if the statistic is outside the interval :- -2.685 to 2.685

b) Test statistic t = x - / (s/n)
= 12-11/(5/10)
= 0.6324
c) With significance level of 0.025 and degree of freedom of 9, the t-critical values are :- -2.685 to 2.685
The test statistic : 0.6324 is greater than right t-critical value : 2.685, and therefore falls in the reject region
Decision : REject null or Reject H0: = 11.
There is sufficient evidence to warrant the rejection of the null hypothesis that: H0: 11

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