Math 227 Sp ‘08 Instr: Wong Ch7&8 Practice Test Name: _________________________
#1
2pts
each
True or False
__________ (a) As the sample size increases, the margin of error increases.
__________ (b) The best point estimate for the population mean  from a normal
distribution is x .
__________ (c) A 99% confidence interval for  is wider than a 95% confidence
interval for .
__________ (d) Samples must be randomly selected for an interval estimation.
__________ (e) The significance level  is the maximum tolerable risk of
incorrectly rejecting Ho.
__________ (f) The shape of z distribution depends on the sample size n.
__________ (g) The claim and Ho are always the same.
__________ (h) A small p-value indicates that the observed value of the test
statistic lies far away from the hypothesized value of .
#2
4pts
Find Z / 2 for the 99% confidence interval.
#3
4pts
Find t / 2 for the 90% with n = 19.
#4
5pts
Find the p-value for a two tailed test with observed z = -1.76.
#5
4pts
Find the p-value for a left tailed test with observed t = 2.718 and n = 11.
#6
7pts
A study of 40 English composition professors showed that they spent, on average,
12.6 minutes correcting a student’s term paper.
(a) Construct a 90% confidence interval for the average time of all English
composition professors spent in correcting a student’s term paper.
Assume  = 2.5 minutes.
3pts
(b) What does “90% confident” mean?
#7
7pts
A researcher is interested in estimating the average salary of police officers in a large
city. She wants to be 95% sure that her estimate is correct. If  = $1050, how large of
a sample should be taken if he wants to estimate the true mean correct to within $200.
#8
7pts
In a study of 10 insurance sales reps from a certain large city, the average of the
grouped was 48.6 years old, and the standard deviation was 4.1 years. Find the 95%
confidence interval of the population mean of all insurance sales reps in that city.
#9
7pts
In a study of 614 family-business owners, 399 responded that the business was started
by the current owners. Find a 90% confidence interval for the proportion p of all family
businesses that were started by the current owners.
#10
7pts
A survey by Brides magazine found that 7 out of 10 brides are planning to take the
surname of their new husband. How large a sample is needed to estimate the true
proportion p within 3% with 95% confidence?
#11 It has been reported that 26% of children in the United States live in homes where
12pts there is a single parent. A school administrator claimed that less than 26% of children
in her school district lived in homes with a single parent. In a sample of 225 children,
54 of them lived in a home with a single parent. Test the administrator’s claim using a
5% level of significance.
#12
A new laboratory technician read a report that the average number of students using
the computer laboratory per hour was 16. To test this hypothesis, he selected a day at
random and kept track of the number of students who used the lab over an eight-hour
period. The results were as follows:
20 24 18 16 16 19 21 23
3pts
a) Give the null and alternative hypotheses for the test.
4pts
b) Use a calculator to calculate x and s.
3pts
c) Calculate the test statistic.
4pts
d) Calculate the p-value for the test statistic.
3pts
e) State your conclusion