Question

In a USA Today survey, 20.8% of 144 respondents said that they aspire to have their boss’s job. Construct a 95% confidence interval estimate of all workers who aspire to have their boss’s job by completing the following questions. (Triola, 2014)

Identify the following:

= ______ (0.5 points) = ______ (0.5 points)

Draw the standard normal curve graph for the 95% confidence interval (1 point). Calculate the z_α/2 and include it in the graph (1 point for listing the z_α/2, 2 points for including the calculations used to obtain the z_α/2).

Calculate the margin of error. (1 point for answer, 2 points for showing the calculations you used to come up with the answer)

Calculate the confidence interval. [1 point for answer, 2 points for showing the work you used to come up with the answer (e.g., the formula calculations if done by hand OR the key sequence and numbers entered if you used the graphing calculator)]

Note: If you are using the graphing calculator, you will need to determine x (the total number of successes). In doing so, you will get a decimal. Round this decimal up to the nearest whole number BEFORE entering it into your graphing calculator.

Interpret the confidence interval. (1 point)

Answer 1

Solution:-

a)

The standard normal curve graph for the 95% confidence interval is

The z_α/2 = + 1.96

b) Margin of error is 0.06629

M.E = 0.06629

c) The the confidence interval is C.I = (0.1417, 0.2743).

C.I = 0.208 + 0.06629

C.I = (0.1417, 0.2743)