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For the hypotheses below, test a = 0.025 with n= 100 and p = 0.69. State

a. the decision rule in terms of the critical value of the test statistic. 
b. the calculated value of the test statistic. 
c. the conclusion

H0: pi >= 0.78
HA:pi < 0>

a. This is a one-tailed test of the population proportion. The decision rule is to reject the null hypothesis if the calculated value of the test statistic, z, is
less than the critical value, z= - 1.96. O


c. Check the requirement for a hypothesis test for a proportion 
satisfied.

In this situation, np = 78 is greater than 5 and n(1-P) = 22 is greater than 5. Thus, the requirement is satisfied. 

What is the proper conclusion?
Because the test statistic is less than the critical value, reject Ho. There is
sufficient evidence to conclude that the population proportion is less than 0.78.
 

The problem is testing the hypothesis that the proportion is less that 0.78, 
The z test and the normal distribution should be used. 

The formula for the z test for proportion is 

z = (p_hatch - p)/sqrt(p * (1 - )/n)

p is the hypothesized population proportion. 

z = (0.69 - 0.78)/sqrt(078 * (1 - 0.78)/100) = -0.217


Because this is a one-tailed test statistic, 

Reject the null hypothesis if the test statistic calculated above is less than the critical value of -1.96. 


The conclusion is not to reject the null hypothesis. 

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