Question

The Avon Longitudinal Study of Parents and Children (ALSPAC) included approximately 14,000 children born between 1991 and 1992 in southwest England, and was intended to investigate a wide range of influences on the health and development of children. The data reported here investigate the relationship between being bullied at age 13, which includes incidents such as the taking of personal belongings; being threatened, blackmailed, hit, or beat up; being called nasty names, having lies told about them, or the like; and depression at 18 years of age. From the original cohort, 3898 children had data on both the frequency of being bullied and later depression. The table shows the results. Never Frequency of Being Bullied Occasionally Frequently 103 101 1343 5 82 Depressed Not depressed 1762 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! We can also do several significance tests to compare the frequencies of having been bullied for those 18-year-olds who suffer and do not suffer from depression. (a) Is there a significant difference between the proportions of being bullied occasionally at age 13 for those 18-year-olds who suffer and do not suffer from depression? Give the z statistic and P-value. (Enter the statistic rounded to two decimal places and the P-value rounded to four decimal places.) z = -0.77 P-value (b) Is there a significant difference between the proportions of being bullied frequently at age 13 for those 18-year olds who

Answer 1

a) For Depressed:

n1 = 97+103+101 = 301

x1 = 103

p̂1 = x1/n1 = 0.3422

For Not depressed:

n2 = 1762+1343+582 = 3687

x2 = 1343

p̂2 = x2/n2 = 0.3643

Null and Alternative hypothesis:

Ho : p1 = p2

H1 : p1 ≠ p2

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (103+1343)/(301+3687) = 0.3626

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.3422 - 0.3643)/√[0.3626*0.6374*(1/301+1/3687)] = -0.77

p-value = 2*(1-NORM.S.DIST(ABS(-0.77), 1)) = 0.4440

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b)

For Depressed:

n1 = 301, x1 = 101, p̂1 = x1/n1 = 0.3355

For Not depressed:

2:n2 = 3687, x2 = 582, p̂2 = x2/n2 = 0.1579

Null and Alternative hypothesis:

Ho : p1 = p2

H1 : p1 ≠ p2

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (101+582)/(301+3687) = 0.1713

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.3355 - 0.1579)/√[0.1713*0.8287*(1/301+1/3687)] = 7.87

p-value = 2*(1-NORM.S.DIST(ABS(7.8683), 1)) = 0.0000