Fall 2008 Statistics Venable TEST 3
PRACTICE TEST 3
Please show all work - even work done by calculator. Please show all steps
in hypothesis test and p-value problems.
1. A sample of 400 workers selected from California showed that they earn an
average of $685 per week. The population standard deviation is known to be
$125. Construct a 95% confidence interval for the mean weekly earnings of
all workers in California.
2. A manager of a driving school claims that the mean time taken to learn
how to drive a car is 8.0 hours for all new drivers. A sample of 16 new
drivers showed that the mean time taken by them to learn how to drive a
car is 9.5 hours with a population standard deviation of 1.607 hours. Find
the p-value for the test that the mean time taken to learn how to drive a car
is greater than 8.0 hours. Assume that the population from which the
sample is drawn is normally distributed.
3. In a poll of 1500 adults, 450 adults said that they live a stressful life.
Construct a 99% confidence interval for the proportion of all adults who live
a stressful life.
4. A researcher wants to estimate the mean income of all physicians in the city
at a 95% confidence level. The standard deviation of the incomes of all
physicians in this city is $17,500. What sample size is required to obtain an
estimate that is within $5000 of the population mean?
5. A department store claims that at least 45% of persons who visit this store
make a purchase. In a sample of 400 persons who visited this store, 37%
made a purchase. Test at the 5% significance level if the claim of the
management is true.
6. A sample of 1000 persons showed that 24% of them own stocks. Construct a
95% confidence interval for the proportion of all persons who own stocks.
7. In 1990, the mean cost of a hotel room in the United States was $125 per day. A
recent sample of 25 hotels showed that the mean cost of a hotel roon1 is $138
per day with a standard deviation of $26. Test at the 2.5% significance level if
the current mean cost of a hotel room is higher than $125. Assume that the
population from which the sample is drawn is normally distributed.
8. A random sample of 28 students selected from a middle school showed that they
spend an average of 45 minutes on homework per day with a standard deviation
of 10 minutes. Assume that the time spent on homework per day by all students
at this school have an approximate normal distribution. Construct a 90%
confidence interval for the mean time spent on homework per day by all
students at this school.
9. A researcher claims that the starting mean salary for new college graduates is
$26,700. A sample 'of 100 recent college graduates showed that their mean
starting salary is $28,200. The population standard deviation is $2700. Test
at the 5% significance level if the mean starting salary of new college
graduates is different from $26,700.
10. The mean price of all college text books was $102 in 2006. The population
standard deviation is known to be $11. A sample of 34 college textbooks
take this year gave a mean price of $107. Find the p-value for the test that the
current mean price of all textbooks is greater than $102.