Question

A random sample of n = 755 US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages,32 with standard error about 6.1.a. Use the information from the sample to give the best estimate of the population parameter. b. Find a 95% confidence interval for the mean number of text messages.

Answer 1

Answer:

a) $\mu = \bar{x} = 41.5$

b) 95% Confidence interval:  (29.5,53.5)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 755

Sample mean = 41.5

Standard Error = 6.1

a) estimate of the population parameter

Parameter of interest:

Mean number of text messages sent or received per day

The population mean is best estimated by the sample mean

$\mu = \bar{x} = 41.5$

b) 95% confidence interval for the mean number of text messages.

95% Confidence interval:

$\mu \pm z_{critical}(\text{Standard error})$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

$41.5 \pm 1.96(6.1)\\ = 41.5 \pm 11.956\\ = (29.544,53.456)\\ \approx (29.5,53.5)$