A research program used a representative random sample of men and women to gauge

Question

A research program used a representative random sample of men and women to gauge the size of the personal network of older adults. Each adult in the sample was asked to "please name the people you have frequent contact with and who are also important to you." The responses of 2,824 adults in this sample yielded statistics on network size, that is, the mean number of people named per person was x overbarxequals=14.4, with a standard deviation of sequals=9.8 Complete parts a through d. Give an interval estimate for . Use a confidence coefficient of 0.95.

Explanation / Answer

From information given, sample mean, xbar=14.4, sample standard deviation, s=9.8, sample size, n=2824. Sample size is large and population standard deviation is unknown. Assume, the data had been drawn from a randomized survey, and respondents are likely to be independent. The 2824 adults are less than 10% of all adults. The sample size is large, hence, the distribution of number of people named per person is normally distributed. Therefore, all the three conditions-randomization condition, 10% condition and nearly normal condition are successfully met. For large sample and unknwon population standard deviation, use student's t model with n-1=2824-1=2823 degrees of freedom and find a one-sample t interval.

The 95% confidence interval for population mean number of people named, mu=xbar+-t(s/sqrt n), where, t denotes t critical at alpha/2 [alpha=0.05, alpha/2=0.05/2=0.025]

=14.4+-1.96(9.8/sqrt 2824)

=(14.038,14.762)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.