According to a sociologist's research on U.S. residents' habits regarding religious faith, 38% of U.S. residents attend a religious service (any denomination) at least once per month. Suppose 310 U.S. residents are sampled. (Give results accurate to at least 4 decimal places.) a. Of the 310 people sampled, 132 respond that they attend a religious service at least once per month. What is the sample statistic p? = 0.4258 08 b. Under the assumption that the sociologist's claim that 38% of U.S. residents attend a religious service at least once per month is valid, what is the probability that the survey in part (a) would result in a p that is at least as high as the one found? c. Under the assumption that the sociologist's claim that 38% of U.S. residents attend a religious service at least once per month is valid, what is the probability that the survey in part (a) would result in a ô that is between 37% and 40%?
According to a sociologist's research on U.S. residents' habits regarding religious faith, 38% of U.S. residents attend a religious service (any denomination) at least once per month. Suppose 310 U.S. residents are sampled. (Give results accurate to at least 4 decimal places.) a. Of the 310 people sampled, 132 respond that they attend a religious service at least once per month. What is the sample statistic p? = 0.4258 08 b. Under the assumption that the sociologist's claim that 38% of U.S. residents attend a religious service at least once per month is valid, what is the probability that the survey in part (a) would result in a p that is at least as high as the one found? c. Under the assumption that the sociologist's claim that 38% of U.S. residents attend a religious service at least once per month is valid, what is the probability that the survey in part (a) would result in a ô that is between 37% and 40%?
MATLAB: An Introduction with Applications
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![### Sociological Study on Religious Service Attendance in the U.S.
#### Overview
A sociologist conducted a study on U.S. residents' habits regarding religious faith. The research claims that 38% of U.S. residents attend a religious service (of any denomination) at least once per month.
#### Study Details
- **Sample Size:** 310 U.S. residents were surveyed.
- **Reported Attendance:** Out of the 310 people sampled, 132 indicated they attend a religious service at least once per month.
#### Questions and Calculations
**a. Sample Statistic Calculation**
To determine the sample statistic \(\hat{p}\):
\[ \hat{p} = \frac{132}{310} = 0.4258 \]
**b. Probability Analysis**
Under the assumption that 38% of U.S. residents attend a religious service at least once per month, calculate the probability that a survey would result in a \(\hat{p}\) at least as high as 0.4258.
**c. Range Analysis**
Calculate the probability that the survey would result in a \(\hat{p}\) between 37% and 40% under the same initial assumption.
### Explanation of the Diagrams
This educational content presents a scenario where statistical analysis is required to verify claims about religious service attendance. The section involves calculating probabilities using the sample statistic obtained from survey data. Students are encouraged to use statistical methods to approach the problem, common in testing hypotheses in sociology and statistics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8e55570-c6c3-4fab-97f3-842970d4ad84%2Ff8409a29-783a-456d-b9de-89c7ea3ea128%2F5je0b8f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Sociological Study on Religious Service Attendance in the U.S.
#### Overview
A sociologist conducted a study on U.S. residents' habits regarding religious faith. The research claims that 38% of U.S. residents attend a religious service (of any denomination) at least once per month.
#### Study Details
- **Sample Size:** 310 U.S. residents were surveyed.
- **Reported Attendance:** Out of the 310 people sampled, 132 indicated they attend a religious service at least once per month.
#### Questions and Calculations
**a. Sample Statistic Calculation**
To determine the sample statistic \(\hat{p}\):
\[ \hat{p} = \frac{132}{310} = 0.4258 \]
**b. Probability Analysis**
Under the assumption that 38% of U.S. residents attend a religious service at least once per month, calculate the probability that a survey would result in a \(\hat{p}\) at least as high as 0.4258.
**c. Range Analysis**
Calculate the probability that the survey would result in a \(\hat{p}\) between 37% and 40% under the same initial assumption.
### Explanation of the Diagrams
This educational content presents a scenario where statistical analysis is required to verify claims about religious service attendance. The section involves calculating probabilities using the sample statistic obtained from survey data. Students are encouraged to use statistical methods to approach the problem, common in testing hypotheses in sociology and statistics.
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