Question

1) In 1998, a random sample of 1036 Americans were asked if they owned a cell phone and 881 said they owned a cell phone. Find the sample proportion, rounded to two decimal places.

pˆ =

2) Construct a 95% confidence interval for the population proportion, first by hand, using the formula, where z* is the z-score associated with a 95% confidence level and qˆ =1− pˆ . Use your estimated sample

proportion from the previous question. Show your work in the space provided.⎛ * pˆqˆ * pˆqˆ⎞

Confidence interval: _________________________________

3) What is the 95% confidence interval given by your calculator? (Use 1-PropZInt.) Confidence interval: ___________________________
Check that this is consistent with your first interval. (It will be slightly off due to rounding.)

4) Interpret your interval in terms of the problem. Note: Your interpretation should include the confidence level, the interval, and the population parameter that is being estimated. (See “Writing the Interpretation” on page 392.) Be as detailed as possible when describing the population parameter.

⎜ pˆ − z n , pˆ + z n ⎟ ⎝⎠

Answer 1

1)

The sample proportion is

2)

3)

Following is the screen shot of calculator after entering data:

Following is the output by entering on calculate:

The required confidence interval is (0.83, 0.87).

4)

We are 95% confident that true proportion who owned a cell phone is lie in the interval (0.83, 0.87).