Question

a sample of 17,taken from a normally distributed population has a sample mean of 96.36and a sample standard deviation of 6.30.Suppose that we have adopted the null hypothesis that the actual population mean is greater than or equal to 99. that is Ho is that ≥99 and we want to test the alternative hypothesis Ha that µ <99 with level of significance a= 0.1

a ) what type of test would be appropriate on this situation

b) what is the critical valu ?( for a two tailed test give the postive value)

c) what is computed test statistic

d. based on your test statistic and the decision rule you have decided upon what can we conclude about Ho

Answer 1

(a) Since population standard deviation is unknown and n < 30, we use an independent samples t test.

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(b) This is a single tailed (left tailed) test, with df = n - 1 = 16.

t critical at = 0.10 is = -1.337

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(c) The Test Statistic: The test statistic is given by the equation:

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(d) The Decision Rule:   If t observed is < -t critical, Then Reject H0.

The Decision: Since t observed (-1.73) is < t critical (-1.337), We Reject H0.

The Conclusion: There is sufficient evidence at the 90% significance level to support the claim that the population mean is less than 99.

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