Dr. Page believes that going through a training program will decrease weekly exercise. College students exercise an average of 2.2 days a week with a variance of 2.25 days. Dr. Page's sample of 28 students exercise an average of 1.6 days a week. What can be concluded with an α of 0.01?
a) What is the appropriate test statistic?
---Select one--- (na, z-test, one-sample t-test, independent-samples t-test, or related-samples t-test)
b)
Population:
---Select one--- ((exercise), college students, days in the week, students, or individuals exposed to the training program)
Sample:
---Select one--- ((exercise), college students, days in the week, students, or individuals exposed to the training program)
c) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select one--- (Reject H0 or Fail to reject H0)
d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]
e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and select "na" below.
d =  ;   ---Select one--- (na, trivial effect, small effect, medium effect, or large effect)
r² =  ;   ---Select one--- (na, trivial effect, small effect, medium effect, or large effect)
f) Make an interpretation based on the results.

a. Individuals that went through the training program did significantly more exercise than college students.

b. Individuals that went through the training program did significantly less exercise than college students.    

c. The training program has no significant effect on weekly exercise.

Q.Explain the flaws in the following analysis or conclusion. (Note that this is not about chi-squared test per se, perhaps, it is about what a statistical analysis (hypothesis testing in this case) can tell us and what it cannot)

Background - The Scholarship Committee comprises 3 faculty members, one of whom is Professor X. Professor X also wrote recommendation letter for 5 students who took his class earlier and four of them were awarded scholarships (out of a total of six scholarships awarded to graduate students). A student who applied but was not awarded a scholarship accused Professor X of favoritism, claiming that he/she was denied a scholarship despite having a very high GPA because he/she did not take class under Professor X and had declined him/her a recommendation letter. The student then did following statistical analysis as an evidence of favoritism .

The student runs a Chisq-test and his result shows not independent between students who took class under Professor X and Students got scholarship.

H0: students who get scholarship is independent with whether they have taken class under Professor X

H1: not independent

# Let total number of students who applied for scholarship is 70, and only 5 people get the scholarship, conservatively estimate only
3 out of 5 students took Class with ProfessorX, the other two selected did not take Class with ProfessorX

# chisquare test shows the p-value <0.05, thus we reject H0 at .05 level and conclude students who got scholarship was affected by whether they have class under Professor X

#student in addition tests , how about the total applicants were 60, or 80?
and find out either case we reject H0, they are not independent.

Q.Explain the flaws in the following analysis or conclusion. (Note that this is not about chi-squared test per se, perhaps, it is about what a statistical analysis (hypothesis testing in this case) can tell us and what it cannot) Background - The Scholarship Committee comprises 3 faculty members, one of whom is Professor X. Professor X also wrote recommendation letter for 5 students who took his class earlier and four of them were awarded scholarships (out of a total of six scholarships awarded to graduate students). A student who applied but was not awarded a scholarship accused Professor X of favoritism, claiming that he/she was denied a scholarship despite having a very high GPA because he/she did not take class under Professor X and had declined him/her a recommendation letter. The student then did following statistical analysis as an evidence of favoritism . The student runs a Chisq-test and his result shows not independent between students who took class under Professor X and Students got scholarship. H0: students who get scholarship is independent with whether they have taken class under Professor X H1: not independent # Let total number of students who applied for scholarship is 70, and only 5 people get the scholarship, conservatively estimate only 3 out of 5 students took Class with ProfessorX, the other two selected did not take Class with ProfessorX # chisquare test shows the p-value <0.05, thus we reject H0 at .05 level and conclude students who got scholarship was affected by whether they have class under Professor X #student in addition tests , how about the total applicants were 60, or 80? and find out either case we reject H0, they are not independent.

Q.Explain the flaws in the following analysis or conclusion. (Note that this is not about chi-squared test per se, perhaps, it is about what a statistical analysis (hypothesis testing in this case) can tell us and what it cannot) Background - The Scholarship Committee comprises 3 faculty members, one of whom is Professor X. Professor X also wrote recommendation letter for 5 students who took his class earlier and four of them were awarded scholarships (out of a total of six scholarships awarded to graduate students). A student who applied but was not awarded a scholarship accused Professor X of favoritism, claiming that he/she was denied a scholarship despite having a very high GPA because he/she did not take class under Professor X and had declined him/her a recommendation letter. The student then did following statistical analysis as an evidence of favoritism . The student runs a Chisq-test and his result shows not independent between students who took class under Professor X and Students got scholarship. H0: students who get scholarship is independent with whether they have taken class under Professor X H1: not independent # Let total number of students who applied for scholarship is 70, and only 5 people get the scholarship, conservatively estimate only 3 out of 5 students took Class with ProfessorX, the other two selected did not take Class with ProfessorX # chisquare test shows the p-value <0.05, thus we reject H0 at .05 level and conclude students who got scholarship was affected by whether they have class under Professor X #student in addition tests , how about the total applicants were 60, or 80? and find out either case we reject H0, they are not independent.

A study of identity theft looked at how well consumers protect themselves from this increasingly prevalent crime. The behaviors of 61 college students were compared with the behaviors of 55 nonstudents. One of the questions was "When asked to create a password, I have used either my mother's maiden name, or my pet's name, or my birth date, or the last four digits of my social security number, or a series of consecutive numbers." For the students, 22 agreed with this statement while 26 of the nonstudents agreed.

(a) Display the data in a two-way table.

Perform the chi-square test. (Round your χ² to three decimal places and round your P-value to four decimal places.)

Summarize the results.

We cannot conclude at the 5% level that students and nonstudents differ in the response to this question.We can conclude at the 5% level that students and nonstudents differ in the response to this question.    

(b) Reanalyze the data using the methods for comparing two proportions that we studied in the previous chapter. Compare the results and verify that the chi-square statistic is the square of the z statistic. (Test students who agreed minus nonstudents who agreed. Round your z to two decimal places and round your P-value to four decimal places.)

(c) The students in this study were junior and senior college students from two sections of a course in Internet marketing at a large northeastern university. The nonstudents were a group of individuals who were recruited to attend commercial focus groups on the West Coast conducted by a lifestyle marketing organization. Discuss how the method of selecting the subjects in this study relates to the conclusions that can be drawn from it.

At Rio Salado College, it was observed that 34% of the students were still classified as dependents on their parents. However, in the honors program for students, 172 out of 418 students are dependents. The administrators want to know if the proportion of dependent students in the honors program is significantly different from the proportion for the school district. Test at the α=.05 level of significance.

What is the hypothesized population proportion for this test?
p=
(Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.)

Based on the statement of this problem, how many tails would this hypothesis test have?

• one-tailed test
• two-tailed test

Choose the correct pair of hypotheses for this situation:

Using the normal approximation for the binomial distribution (without the continuity correction), was is the test statistic for this sample based on the sample proportion?
z=
(Report answer as a decimal accurate to 3 decimal places.)

You are now ready to calculate the P-value for this sample.
P-value =
(Report answer as a decimal accurate to 4 decimal places.)

This P-value (and test statistic) leads to a decision to...

• reject the null
• accept the null
• fail to reject the null
• reject the alternative

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the assertion that there is a different proportion of dependent students in the honors program.
• There is not sufficient evidence to warrant rejection of the assertion that there is a different proportion of dependent students in the honors program.
• The sample data support the assertion that there is a different proportion of dependent students in the honors program.
• There is not sufficient sample evidence to support the assertion that there is a different proportion of dependent students in the honors program.

A study of identity theft looked at how well consumers protect themselves from this increasingly prevalent crime. The behaviors of 63 college students were compared with the behaviors of 58 nonstudents. One of the questions was "When asked to create a password, I have used either my mother's maiden name, or my pet's name, or my birth date, or the last four digits of my social security number, or a series of consecutive numbers." For the students, 24 agreed with this statement while 29 of the nonstudents agreed.

(a) Display the data in a two-way table.

Perform the chi-square test. (Round your χ² to three decimal places and round your P-value to four decimal places.)

Summarize the results.

We can conclude at the 5% level that students and nonstudents differ in the response to this question.We cannot conclude at the 5% level that students and nonstudents differ in the response to this question.   

(b) Reanalyze the data using the methods for comparing two proportions that we studied in the previous chapter. Compare the results and verify that the chi-square statistic is the square of the z statistic. (Test students who agreed minus nonstudents who agreed. Round your z to two decimal places and round your P-value to four decimal places.)

(c) The students in this study were junior and senior college students from two sections of a course in Internet marketing at a large northeastern university. The nonstudents were a group of individuals who were recruited to attend commercial focus groups on the West Coast conducted by a lifestyle marketing organization. Discuss how the method of selecting the subjects in this study relates to the conclusions that can be drawn from it.

A study of identity theft looked at how well consumers protect themselves from this increasingly prevalent crime. The behaviors of 61 college students were compared with the behaviors of 58nonstudents. One of the questions was "When asked to create a password, I have used either my mother's maiden name, or my pet's name, or my birth date, or the last four digits of my social security number, or a series of consecutive numbers." For the students, 23 agreed with this statement while 29 of the nonstudents agreed.

(a) Display the data in a two-way table.

Perform the chi-square test. (Round your χ² to three decimal places and round your P-value to four decimal places.)

Summarize the results.

We cannot conclude at the 5% level that students and nonstudents differ in the response to this question.We can conclude at the 5% level that students and nonstudents differ in the response to this question.    

(b) Reanalyze the data using the methods for comparing two proportions that we studied in the previous chapter. Compare the results and verify that the chi-square statistic is the square of the z statistic. (Test students who agreed minus nonstudents who agreed. Round your z to two decimal places and round your P-value to four decimal places.)

(c) The students in this study were junior and senior college students from two sections of a course in Internet marketing at a large northeastern university. The nonstudents were a group of individuals who were recruited to attend commercial focus groups on the West Coast conducted by a lifestyle marketing organization. Discuss how the method of selecting the subjects in this study relates to the conclusions that can be drawn from it.

Sleep (Raw Data, Software Required):
Assume the general population gets an average of 7 hours of sleep per night. You randomly select 35 college students and survey them on the number of hours of sleep they get per night. The data is found in the table below. You claim that college students get less sleep than the general population. That is, you claim the mean number of hours of sleep for all college students is less than 7 hours. Test this claim at the 0.10 significance level.

Sleep (Raw Data, Software Required): Assume the general population gets an average of 7 hours of sleep per night. You randomly select 35 college students and survey them on the number of hours of sleep they get per night. The data is found in the table below. You claim that college students get less sleep than the general population. That is, you claim the mean number of hours of sleep for all college students is less than 7 hours. Test this claim at the 0.10 significance level.

(a) What type of test is this? This is a right-tailed test. This is a left-tailed test. This is a two-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places. t x =

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places. P-value =

(d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0

(e) Choose the appropriate concluding statement.

a. The data supports the claim that college students get less sleep than the general population.

b. There is not enough data to support the claim that college students get less sleep than the general population.

c. We reject the claim that college students get less sleep than the general population.

d. We have proven that college students get less sleep than the general population.

DATA ( n = 35 )

Sleep per Night
College Students