SOLUTION: Pharmaceutical companies promote their prescription drugs using television advertising. In a survey of 75 randomly sampled television viewers, 6 indicated that they asked their phy

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Question 1193396: Pharmaceutical companies promote their prescription drugs using television advertising. In a survey of 75 randomly sampled television viewers, 6 indicated that they asked their physician about using a prescription drug they saw advertised on TV.
a. What is the point estimate of the population proportion? (Round your answers to 1 decimal places.)

b. What is the margin of error for a 95% confidence interval estimate?

Answer by math_tutor2020(3817) (Show Source):
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Answers:
a) 0.1
b) 0.0614

The answer to part (a) had been rounded (it was initially 0.08)
The answer for part (b) is approximate. Round it however you need to.
The more accurate value is roughly 0.061399431050567

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Explanations:

a)

The population proportion p is best estimated by the sample proportion phat (symbol )
We pronounce it as "p-hat" since the letter p has a hat on top.
The point estimate is the center of the confidence interval.

x = number of people who asked their physician about a drug they saw on tv
x = 6
n = sample size
n = 75

So,
phat = x/n
phat = 6/75
phat = 0.08
phat = 0.1 when rounding to one decimal place

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b)

Use a table like this one
https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
to look at the bottom row marked in blue (it starts with Z)
The value 1.960 is just above the 95% confidence level.

What this means is P(-1.960 < Z < 1.960) = 0.95 approximately.
z = 1.960 is the approximate critical value for a 95% confidence level.

E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 1.960*sqrt(0.08*(1-0.08)/75)
E = 0.061399431050567
E = 0.0614
This value is approximate.