A recent survey asked how many hours within the average day

A recent survey asked \"how many hours, within the average day do you watch television?

Sample size: 1324,

Mean : 2.9800,

SD : 2.6600,

S error:0.0731

95% Confidence Limit (2.8366, 3.1234)

Qa Interpret the 95% confidence interval in detail

b. How was the standard error obtained? What does it mean?

c. What do the sample mean and standard deviation suggest about the likely shape of the population distribution?

Solution

a 95 % confidence interval does not mean that there is a 95 % probability that the interval contains the true mean. The interval computed from a given sample either contains the true mean or it does not. Instead, the level of confidence is associated with the method of calculating the interval. The confidence coefficient is simply the proportion of samples of a given size that may be expected to contain the true mean. That is, for a 95 % confidence interval, if many samples are collected and the confidence interval computed, in the long run about 95 % of these intervals would contain the true mean.

b.SEx = s/(n)^1/2

s = standard deviation of sample

n = number of observations in sample

SEx = 2.66/(1324)^1/2

        = 0.73099

       = 0.731

The standard error is an estimate of the standard deviation of a statistic.

C. The Standard Deviation is a measure of how spread out ojects of a sample are.and mean is average of numbers

        .its a normal distribution curve with more than 95 of sample lying between mean - sd and mean + sd because confidence interval lie in that interval so its likely to have a bell shape