SOLUTION: A Gallup poll asked a random sample of 1785 adults, "Did you attend church or synagogue in the last 7 days?" Of the respondents, 690 said, "Yes". Perform a test to see if this give

Question 1006519: A Gallup poll asked a random sample of 1785 adults, "Did you attend church or synagogue in the last 7 days?" Of the respondents, 690 said, "Yes". Perform a test to see if this gives sufficient evidence to support the claim that fewer than 40% of adults regularly attend religious services.
Make sure to complete the steps:
Hypotheses
Model
Mechanics
Conclusion

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Ho=proportion is >=0.40
Ha: proportion is <0.40
alpha =0.05, two tail test
test stat is one sample proportion z=(phat-0.4)/sqrt[p*(1-p)/n]; 695/1785=0.3866 z=(0.3866-0.40)/sqrt[p*(1-p)/n]
critical value is z>=-1.645
Std error is sqrt [(0.4)(0.6/1785}=0.0116
z= -0.0134/0.0116= -1.156
Fail to reject Ho.
The true proportion may be greater than or equal to 0.40
CI (0.368,0.406)
We are 95% confident that the true proportion lies within this interval, which contains the parameter of interest, so again, we cannot reject Ho.
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