Question

1) In a survey, 21 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $49 and standard deviation of $3. Find the margin of error at a 95% confidence level. Give your answer to two decimal places.

2) The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 65.5 for a sample of size 445 and standard deviation 12.8.
Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level).
Enter your answer accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
__ < μ < __

3) At a traffic stop on a Saturday night 29% of 51 drivers were intoxicated. What is the 80% confidence interval for the population proportion of drunk drivers?
Give your answers as decimals, to two places.

__ < p < __

Answer 1

1)

As the population s.d is unknown here we will use t distribution to estimate the margin of error

Degrees of freedom is = n-1 = 20

For 20 dof and 95% confidence level critical value t from t table is 2.09

Margin of error (MOE) = t*s.d/√n = 2.09*3/√21 = 1.37

2)

Given mean = 65.5

N = 455

Smd = 12.8

Degrees of freedom is = n-1 = 454

For 454 dof and 99% confidence level critical value.t from t distribution is 2.59

Margin of error (MOE) = t*s.d/√n = 2.59*12.8/√455 = 1.552

Interval is given by (mean - moe, mean + moe)

[63.948, 67.052].

You can be 99% confident that the population mean (μ) falls between 63.948 and 67.052.

63.9<u<67.1