Should be relatively easy if you if you are good at stats. Don't be intimidated by the big problem.

The Gallup organization has been tracking religious attitudes and practices in the United States since 1937, when they reported that 73% of the US claimed membership in a church. That number went down to 69% in 2000 and down again to 62% in 2010. A recent report stated that only half of US adults now consider themselves members of a church. The report was based on a study of 6,000 randomly selected US adults which resulted in 2,940 who said that they belonged to a church. Is the proportion of US adults who belong to a church different than 50%? Use alpha=0.05.

Part A. Test of Significance

STATE: At the = 0.05 level, is there sufficient evidence to conclude that the proportion of US adults who belong to a church different than 50%?

1. State the name of the appropriate test procedure you will use (e.g., one-sample t test for means).
2. Describe the parameter of interest in the context of the problem.
3. State the null and alternative hypotheses.
4. Write down the significance level.

SOLVE:

1. List and check the conditions for the test procedure you named above.
2. Obtain the value of the sample proportion. Round to 4 decimal places if necessary.
3. Write the calculated test statistic (including your calculations) and its associated P-value using the appropriate table, not from statistical software. Do not round any numbers used in your calculations for the test statistic, and round your final answer for the test statistic to two decimal places.

CONCLUDE:

Answer the question posed in the STATE step in context. Done by including these three parts in your conclusion:

Compare P-value with Decide whether to reject or fail to reject the null hypothesis State your conclusion in context

______________________________________________________________________________________

Part B. Confidence Interval Estimation

STATE: What is a 90% confidence interval estimate for the proportion of all of US adults who belong to a church?

PLAN: State the name of the appropriate estimation procedure (e.g. one-sample t confidence interval for estimating the mean difference).

Note: You have already described the parameter being estimated in Part A, so you don't have to repeat it here.

SOLVE:

1. You have already listed the conditions, but now check the condition for the normality of the sampling distribution of P^ for confidence interval estimation.
2. Write down the confidence level and the z* critical value.
3. Calculate the confidence interval in interval form. Be sure to show your work. Round your answer to three decimal places.

CONCLUDE:

Interpret your confidence interval in context. (3 pts) Done by including these three parts in your conclusion:

Level of confidence Parameter of interest in context The interval estimate