Question

A study was conducted concerning blood pressure of 65-year-old men with glaucoma. The average blood pressure in 65-year-old men is 110mmHg. In the study, 144 65-year-old men with glaucoma are randomly selected and the sample mean blood pressure was 120 mmHg and the sample standard deviation is 15 mmHg. Test the claim that this sample comes from a population with blood pressure that is 110 mmHg, and state your decision.

Answer 1

Given: = 110, = 120, s = 15, n = 144, = 0.05 (default level)

The Hypothesis:

H0: = 110

Ha: 110

This is a 2 tailed test

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The Test Statistic: Although the population standard deviation is known, n is very large and hence we use the z test.

The test statistic is given by the equation:

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The p Value: The p value (2 Tail) for Z = 8.00, is; p value = 0.0000

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The Critical Value:   The critical value (2 Tail) at = 0.05, Zcritical= +1.96 and -1.96

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The Decision Rule:   If Zobservedis >Zcritical or if Zobserved is < -Zcritical, Then reject H0.

Also if P value is < , Then Reject H0.

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The Decision:   Since Zobserved (8) is > Zcritical (1.96), We Reject H0.

Also since P value (0.0000) is < (0.05) , We Reject H0.

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The Conclusion: There is sufficient evidence at the 95% significance level to warrant rejection of the claim that this sample comes from a population with blood pressure that is 110 mg.

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