Question

In June of 1994 the Nick-at-Nite television network conducted a phone-in survey of its viewers with regard to this question, "Which classic sitcom character, Jeannie from I Dream of Jeannie or Samantha from Bewitched, possessed more magic powers?". Samantha received 810,000 votes and Jeannie received 614,000.

a) Identify the population and the parameter of interest

b) Is this sample a random sample from the population of interest?

c) Find a 97% confidence interval for the population parameter of interest

d) Explain why the confidence interval is so narrow

Answer 1

Result:

In June of 1994 the Nick-at-Nite television network conducted a phone-in survey of its viewers with regard to this question, "Which classic sitcom character, Jeannie from I Dream of Jeannie or Samantha from Bewitched, possessed more magic powers?". Samantha received 810,000 votes and Jeannie received 614,000.

a) Identify the population and the parameter of interest

population : All viewers of Nick-at-Nite television network

parameter of interest: true proportion of viewers who think have more magic powers, Dream of Jeannie or Samantha from Bewitched.

b) Is this sample a random sample from the population of interest?

No, this is a phone-in survey.

c) Find a 97% confidence interval for the population parameter of interest

proportion who likes Samantha = 810000/(810000+614000) =0.56882

Confidence Interval Estimate for the Proportion
Data
Sample Size	1424000
Number of Successes	810000
Confidence Level	97%
Intermediate Calculations
Sample Proportion	0.568820225
Z Value	2.1701
Standard Error of the Proportion	0.0004
Interval Half Width	0.0009
Confidence Interval
Interval Lower Limit	0.5679
Interval Upper Limit	0.5697

97% CI = (0.5679, 5697)

d) Explain why the confidence interval is so narrow.

Since the sample size is large, the standard error becomes very small. Therefore the confidence interval is narrow.