Download Math 52 exam 1 sp 05

Name___________________
Confidence interval problems for Math 52 Spring 2009 ANSWERS
1. A sample of 24 left-handed men was found to have a mean height of 75 inches with a
standard deviation of 1.9 inches. The heights of left-handed men appear to be
normally distributed. Find the 95% confidence interval for the mean height of the
population of left-handed men. Write a conclusion sentence.
df = 23,   .05 in two tails. Use the t-dist because s is known and the confidence
interval is for the population mean.
75  2.069
1.9
1.9
   75  2.069
24
24
74.19756757    75.80243243
We are 95% confident that the mean height of the population for left-handed men is
between 74.2 and 75.8 inches.
2. In preparing to do a study on the proportion of people who use internet gambling
sites, you must determine how many people to survey. If you want to be 99%
confident that the population proportion is within 3 percentage points, how many
people must you survey? Write a conclusion sentence.
2.5752
n
(.25)  1841.8 round up so n = 1842.
.032
We need top sample at least 1842 people to be 99% confident that the sample
proportion is within 3 percentage points.
1
3. If you wanted to estimate the mean amount of beer consumed daily by adults, how
many people must you survey if you want to be 90% confident that your sample is in
error by no more than 0.75 ounces. Based on results from a pilot study you may
assume that the population standard deviation is 2.82 ounces. Write a conclusion
sentence.
2
 1.645*2.82 
n
  38.2567 round up so n = 39.
.75


We need to sample at least 39 people to be 90% confident that our sample mean of
beer consumption is within .75 ounces of the mean.
4. In a recent study of caffeinated beverages; a sample of 42 cans were found to have a
mean of 6.8 grams of caffeine per ounce. We know from previous research that
population of caffeine in such beverages is normally distributed with a standard
deviation of 2.4 grams of caffeine per ounce. Find the 98% confidence interval for
mean amount of caffeine per ounce. Write a conclusion sentence.
Use the normal (z) dist. because the population standard deviation is known and the
confidence interval is for the mean.
6.8  2.33
2.4
2.4
   6.8  2.33
42
42
5.937135667    7.662864333
We are 98% confident that the true mean amount of caffeine per ounce is between 5.9
and 7.7 ounces.
2
5. In a study to determine the cost of Law School degree a random sample of 41 Law
Schools found them to have a mean cost per year of $38,500 with a standard
deviation of $3500. Find a 95% confidence interval for the standard deviation of the
cost per year for all Law Schools. Write a conclusion sentence.
Note: For the problem the standard deviation that was given in the intial problem
was the population standard deviation  , it should have been the sample standard
deviation s.
(41  1)35002
(41  1)35002
 
59.342
24.433
8257220.855    20054843.86
2873.538038    4478.263487
We are 95% confident that the true standard deviation for the cost per year of all
law schools is between $2873.54 and $4478.26
6. A recent study on professional athlete who failed drug tests for steroids found in a
random sample of 350 professional athletes, 75 of the athletes failed the drug test. It
has recently been discovered that there was much more rampant steroid use than in
the past, one of the most commonly used steroids did not lead to a positive drug test
until recently. Find a 99% confidence interval for the population proportion of people
who failed the drug test. Write a conclusion sentence.
 x 75
p 
 .2142857143  .214
n 350
.214  2.575
(.214*.786
(.214*.786
 p  .214  2.575
350)
350)
.1575503347  p  .2704496653
We are 99% confident that the true population proportion of all people who failed
a drug test is between 15.8% and 27.0%
3