"Snoqualmie" is a name shared by a spectacular 268-foot waterfall and a tribe ofNative Americans. The Falls provides a place for the people to worship. In a studyof the significance of the Falls to modern tribal members, surveys of two groups wereperformed. One group consisted of a random sample of members living within thetraditional tribal area, a circle with an approximate radius of 25 miles. The othergroup consisted of a random sample of members living outside this area. Theinvestigators asked questions such as whether a sense of personal renewal was felt atthe Falls, or whether personal healing/cleansing was experienced.The investigators combined responses to the various questions to make a "level ofspiritual encounter index." A chi-square test was used to determine if the distributionsof level of spiritual encounter differs for the two groups. The observed and expectedcounts are summarized in the table below along with the value of the chi-squarestatistic and the associated P-value.
a) State the null and alternative hypotheses for this test.
b) Discuss whether the conditions for a chi-square inference procedure are met forthese data.
c) What should the investigators conclude based on the results of the chi-square test?
d) It is possible that an error (Type I or Type II) could occur. Which error might theinvestigators make, based on your answer in part (c)?
Describe this error in thecontext of the question.

Question

"Snoqualmie" is a name shared by a spectacular 268-foot waterfall and a tribe ofNative Americans. The Falls provides a place for the people to worship. In a studyof the significance of the Falls to modern tribal members, surveys of two groups wereperformed. One group consisted of a random sample of members living within thetraditional tribal area, a circle with an approximate radius of 25 miles. The othergroup consisted of a random sample of members living outside this area. Theinvestigators asked questions such as whether a sense of personal renewal was felt atthe Falls, or whether personal healing/cleansing was experienced.The investigators combined responses to the various questions to make a "level ofspiritual encounter index." A chi-square test was used to determine if the distributionsof level of spiritual encounter differs for the two groups. The observed and expectedcounts are summarized in the table below along with the value of the chi-squarestatistic and the associated P-value.  
a) State the null and alternative hypotheses for this test.
b) Discuss whether the conditions for a chi-square inference procedure are met forthese data.
c) What should the investigators conclude based on the results of the chi-square test?
d) It is possible that an error (Type I or Type II) could occur. Which error might theinvestigators make, based on your answer in part (c)?
 Describe this error in thecontext of the question.

Quizplus · Accepted Answer

The Answer of "Snoqualmie" is a name shared by a spectacular 268-foot waterfall and a tribe ofNative Americans. The Falls provides a place for the people to worship. In a studyof the significance of the Falls to modern tribal members, surveys of two groups wereperformed. One group consisted of a random sample of members living within thetraditional tribal area, a circle with an approximate radius of 25 miles. The othergroup consisted of a random sample of members living outside this area. Theinvestigators asked questions such as whether a sense of personal renewal was felt atthe Falls, or whether personal healing/cleansing was experienced.The investigators combined responses to the various questions to make a "level ofspiritual encounter index." A chi-square test was used to determine if the distributionsof level of spiritual encounter differs for the two groups. The observed and expectedcounts are summarized in the table below along with the value of the chi-squarestatistic and the associated P-value.  
a) State the null and alternative hypotheses for this test.
b) Discuss whether the conditions for a chi-square inference procedure are met forthese data.
c) What should the investigators conclude based on the results of the chi-square test?
d) It is possible that an error (Type I or Type II) could occur. Which error might theinvestigators make, based on your answer in part (c)?
 Describe this error in thecontext of the question.

"Snoqualmie" Is a Name Shared by a Spectacular 268-Foot Waterfall