Question

A sample of size 194, taken from a normally distributed population whose standard deviation is known to be 9.50, has a sample mean of 91.34. Suppose that we have adopted the null hypothesis that the actual population mean is greater than or equal to 93, that is, H0 is that μ ≥ 93 and we want to test the alternative hypothesis, H1, that μ < 93, with level of significance α = 0.05. a) What type of test would be appropriate in this situation? A right-tailed test. A left-tailed test. A two-tailed test None of the above. b) What is the critical value? (for a two-tailed test give the positive value) For full marks your answer should be accurate to at least two decimal places. Critical value: 0 c) What is the computed test statistic? For full marks your answer should be accurate to at least two decimal places. Test statistic: 0 d) Based on your test statistic and the decision rule you have decided upon, what can we conclude about H0? There is sufficient evidence, at the given significance level, to reject H0. There is insufficient evidence, at the given significance level, to reject H0; or we fail to reject H0. There is insufficient evidence to make it clear as to whether we should reject or not reject the null hypothesis

Answer 1

Given : Sample size=n=194

Sample mean=91.34

population standard deviation=

Significance level=

Specified value of the

Hypothesis : Vs

a) The test is left tailed test

b) Critical value :

c) The test statistic under Ho is ,

d) Decision : Here ,

Therefore , reject Ho at level of significance

Conclusion : Hence , there is sufficient evidence at the given significance level.