Question

Young Professional magazine was developed for a target audience of recent college graduates who are in their first 10 years in a business/professional career. In its two years of publication, the magazine has been fairly successful. Now the publisher is interested in expanding the magazine’s advertising base. Potential advertisers continually ask about the demographics and interests of subscribers to Young Professional. To collect this information, the magazine commissioned a survey to develop a profile of its subscribers. The survey results will be used to help the magazine choose articles of interest and provide advertisers with a profile of subscribers. As a new employee of the magazine, you have been asked to help analyze the survey results which had a sample size of 410. The data is summarized below: Quantitative Variables Mean Standard Deviation Age 30.112 4.024 Household Income $74,460 $34,818 Qualitative Variables Count Broadband Access Yes: 256 Have Children Yes: 219 a. Develop 95% confidence intervals for the mean age and household income of subscribers. b. Develop 95% confidence intervals for the proportion of subscribers who have broadband access at home and the proportion of subscribers who have children. c.Would Young Professional be a good advertising outlet for online brokers?Justify your conclusion with statistical data.please provide detailed solution

Answer 1

Given:

For quantitative variables, Age : Mean = 30.112 and SD = 4.024 Household Income :  Mean = $74,460 and SD = $34,818

For qualitative variable, Broadband Access,

Proportion of subscribers who have broadband access at home = 256 / 410 = 0.624 Proportion of  subscribers who have children = 219 / 410 = 0.534

a. 95% confidence intervals for the mean is given by:

Using excel, the t value for 410 - 1 = 409 df is obtained as:

We get, t = 1.966

Substituting the values,

= (30.112 - 0.391, 30.112 + 0.391)

=

Similarly for household income,

Substituting the values,

= (74460 - 3.301, 74460 + 3.301)

=

b. 95% confidence intervals for the proportion is given by

From normal tables,

For subscribers who have broadband access at home, 0.624

Substituting the values,

= ( 0.624 - 1.96 * 0.024, 0.624 + 1.96 * 0.024)

=

For subscribers who have children,

Substituting the values,

=(0.534 - 1.96 * 0.025, 0.534 + 1.96 * 0.025)

=

c. Based on the confidence interval for mean age of the subscribers, , we find that young adults of age around 30 are the potential subscribers.We may thus, based on the 95% confidence interval constructed on the basis of the sample, conclude that Young Professionals would be a good advertising outlet for online brokers.