Question

Demonstrate that you understand the concept of Hypothesis Testing.
? Make a statement about population mean (setup Ho and Ha).
? Describe collected sample data (sample mean, standard deviation, sample size).
? Explain how you will make the decision: does sample data support Ho (accept Ho)
or sample data do not support Ho (reject Ho).

Answer 1

(a)

PROBLEM CONSIDERED: A random sample of 900 members is found to have a mean of 4.45 cm.and standard deviation 2 cm. Can it be reasonably regarded as a sample from a large population whose mean is 5 cm ?

STATEMENT ABOUT POPULATION MEAN:

H0: Null Hypothesis: H0: The sample is drawn from a large population whose mean is 5 cm., i.e., = 5

HA: Alternative Hypothesis: 5

(b)

Collected sample data:

Sample mean = = 4.45

Sample standard deviation = s = 2

Sample size = n = 900

(c)

SE = s/

= 2/ = 0.067

Test statistic is:
Z = ( - )/SE

= (4.45 - 5)/0.067 = - 8.21

Take = 0.05

From Table, critical values of Z = 1.96.

Since the calculated value of Z = - 8.21 is less than critical value of Z = - 1.96, Reject H0.

Conclusion:

The sample data do not support H0 (Reject H0).