The Professor's Response

Hi professor. I keep getting stuck in the same problems. My confusion is when I watch the videos and it display how to do the work on a graphing calculator. Could you please go through problem 58 from 7.6, and show me the steps without the graphing calculator? I could do the earlier problems from that section but 58 and the following few problems Im struggling with when the n is given instead of the ^P .

See the professor's answer below.

Hi Reina,

Use the following data to form a confidence interval for the proportion: n = 3896, x = 702, Clevel = 95%

Step 1: Data n = 3896, x = 702, Clevel = 95%

find p-hat = x / n = 702 / 3896 = 0.1802

q - hat = 1 - p-hat = 1 - 0.1802 = 0.8198

alpha = 1 - CL = 1 - 0.95 = 0.05

Step 2: Critical value Za/2 = Z0.025 = (look up 0.025 on the t-table, then go down to the bottow of that column, the last value is your critical value) = 1.96

Step 3: Margin of Error: E = Za/2*SquareRoot(p-hat* q-hat / n) = 1.96*SquareRoot(0.1802*0.8198 / 3896) = 0.01207

Step 4: (p-hat - E, p-hat + E) = (0.1681, 0.1923)

So, we are 95% confident that the population proportion is between 16.81% and 19.23%.

Hope that helps,

Professor McGuckian