# Testing Hypothesis

Testing Hypothesis. Identify the null hypothesis, alternative hypothesis, test statistics, P-value or critical value (s), conclusion about the null hypothesis, and final conclusion that address the original claim. Use the P-value method unless your instructor specifies otherwise.

A random sample of 100 babies is obtained, and the mean head circumference is found to be 40.6 cm. Assuming that the population standard deviation is known to be 1.6 cm, use a 0.05 significance level to test the claim that the mean head circumference of all two-month-old babies is equal to 40.0 cm.

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Testing Hypothesis. Identify the null hypothesis, alternative hypothesis, test statistics, P-value or critical value (s), conclusion about the null hypothesis, and final conclusion that address the original claim. Use the P-value method unless your instructor specifies otherwise.

A random sample of 100 babies is obtained, and the mean head circumference is found to be 40.6 cm. Assuming that the population standard deviation is known to be 1.6 cm, use a 0.05 significance level to test the claim that the mean head circumference of all two-month-old babies is equal to 40.0 cm.

Answer

H0: The mean head circumference of all two-month-old babies is equal to 40.0 cm.

H1: The mean head circumference of all two-month-old babies is different from 40.0 cm.

The test statistic used is

Significance level

Decision rule: Reject the null hypothesis, if the value is less than the significance level.

Details

Z Test of Hypothesis for the Mean

Data

Null Hypothesis = 40

Level of Significance 0.05

Population Standard Deviation 1.6

Sample Size 100

Sample Mean 40.6

Intermediate Calculations

Standard Error of the Mean 0.16

Z Test Statistic 3.75

Two-Tail Test

Lower Critical Value -1.959963985

Upper Critical Value 1.959963985

p-Value 0.000176835

Reject the null hypothesis

Conclusion: Fails to reject the null hypothesis. The sample provides enough evidence to support the claim that the mean head circumference of all two-month-old babies is different from 40.0 cm.

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