Question

Social media users use a variety of devices to access social networking; mobile phones are increasingly popular. However, is there a difference in the various age groups in the proportion of social media users who use their mobile phone to access social networking? A study showed the following results for the different age groups, assume that 200 social media users for each age group were surveyed.

ORIGINAL DATA

ACCESS TO SOCIAL MEDIA	18-34	35-64	65+	TOTAL
YES	118	72	26	216
NO	82	128	174	384
TOTAL	200	200	200	600

EXPECTED FREQUENCY TABLE

ACCESS	18-34	35-64	65+
YES	72	72	72
NO	128	128	128

FINAL TABLE

ACCESS	18-34	35-64	65+
YES	29.389	0	29.389
NO	16.531	0	45.920

ALPHA = 0.05

D.FREEDOM = 2

XSTAT = 91.840

P-VALUE = 1.12061E-20 (Actually 0)

CRITICAL VALUE = 5.99

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What I need help with is:

If appropriate, use the Marascuilo procedure and alpha=.05 to determine which age groups differ

1. What is the Critical Range number when comparing 18-34 group with 35-64 group?

2. What is the Critical Range number when comparing 18-34 group with 65+ group?

3. What is the Critical Range number when comparing 65+ group with 35-64 group?

4. What is the proportion difference number when comparing 18-34 group with 35-64 group?

------- Then Conclusion

5. What is the conclusion when comparing 18-34 group with 35-64 group?

Select one:

A. The proportions from these two groups are significantly different

B. The proportions from these two groups have no difference

C. The proportions from these two groups have no difference

D. The means from these two groups are significantly different

6. What is the final conclusion on this problem?

Select one:

A. The different age groups have very similar percentage people use their mobile phone access social networking

B. Two groups have different percentage use mobile phone access social networking

C. The factor of whether using mobile phone access social networking in independent with people's age group

D. The different age groups have different percentage people use their mobile phone access social networking

Answer 1

critical range = √critical value * √( pi*(1-pi)/ni + pj*(1-pj)/nj)

1) Critical Range number when comparing 18-34 group with 35-64 group?

Sample Proportions
18-34	118 / 200 = 0.59
35-64	72/200 = 0.36

critical range = √5.99 * √(0.59*(1-0.59)/200 + 0.36(1-0.36)/200) = 0.1189

2) Critical Range number when comparing 18-34 group with 65+ group

Sample Proportions
18-34	0.59
65+	0.13

critical range = √5.99 * √(0.59*(1-0.59)/200 + 0.13(1-0.13)/200) = 0.1031

3)Critical Range number when comparing 65+ group with 35-64 group

Sample Proportions
35-64	0.36
65+	0.13

critical range = √5.99 * √(0.36*(1-0.36)/200 + 0.13(1-0.13)/200) = 0.1014

4)

proportion difference number when comparing 18-34 group with 35-64 group=0.59-0.36=.0.23

5)

if absolute difference > critical range, two groups are significantly different

here, absolute difference = 0.23 > critical range = 0.1189 ,

so, The proportions from these two groups are significantly different

6)

Two groups have different percentage use mobile phone access social networking