Download Chapter 10 Test Review

Chapter 10 Test Review
1) A level C confidence interval for a parameter has two parts:

An interval calculated form the data,
estimate ± margin of error
  
x  z *

 n

A confidence level C, which gives the probability that the interval will capture the true parameter
value in repeated samples.
2) The critical value z* is chosen so that the standard normal curve has area C between –z* and z*.
3) The margin of error of a confidence interval gets smaller (more narrow) as



the confidence level C decreases. (ex: 99% confident is wider than 95% confident)
the population standard deviation  decreases.
the sample size n increases.
4) To find the sample size necessary to obtain a certain margin of error (m.o.e), solve the following
inequality for n:
  
z *
  m.o.e
 n
(always round up for n) See practice problems #2 and #3 for examples.
5) A z test assesses the evidence provided by data against a hypothesis Ho in favor of an alternative
hypothesis Ha.
For additional
practice, try
exercises 10.38,
39, 40, and 42.
6) If the P-value is as small or smaller than a specified value α, the data are statistically significant at
significance level α. (use α = 0.05 unless otherwise stated)
7) Reject Ho for p-values less than α. For p-values greater than α, Fail to Reject Ho.
8) A Type I Error occurs if we reject Ho when it is in fact true. The probability of a Type I Error is α.
9) A Type II Error occurs if we fail to reject Ho when in fact Ha is true.
10) The power of a significance test measures its ability to detect an alternative hypothesis. The power
against a specific alternative is the probability that the test will reject Ho when the alternative is true.
11) There are four ways to increase the power of a test. The two most common are: 1) increase α, or
2) increase the sample size n.
Chapter 10 Test Review Problems
1)
Suppose that the population of the scores of all high school seniors who took the SAT Math test this year
follows a normal distribution with mean  and standard deviation  = 100. You read a report that says,
“on the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a
confidence interval for  is 512.00 ± 25.76.” The confidence level for this interval is
(a) 90%.
(a) 95%.
(b) 99%.
(c) 99.5%.
(e)over 99.9%.
2) Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first
year at a major university. The interval is to have a margin of error of $2, and the amount spent has a normal
distribution with a standard deviation  = $30. The number of observations required is closest to
(a) 25.
(b) 30.
(c) 608.
(d) 609.
(e) 865.
3)
4)
You want to estimate the mean SAT score for a population of students with a 90% confidence interval.
Assume that the population standard deviation is  = 100. If you want the margin of error to be
approximately 10, you will need a sample size of
(a) 16
(b) 271
(c) 38
(d) 1476
A significance test was performed to test the null hypothesis H0: µ = 2 versus the alternative Ha: µ  2.
The test statistic is z = 1.40. The P-value for this test is approximately
(a) 0.16
(b) 0.08
(c) 0.003
(d) 0.92
(e) 0.70
5)
You have measured the systolic blood pressure of a random sample of 25 employees of a
company located near you. A 95% confidence interval for the mean systolic blood pressure for the
employees of this company is (122, 138). Which of the following statements gives a valid interpretation of
this interval?
(a) Ninety-five percent of the sample of employees has a systolic blood pressure between 122 and 138.
(b) Ninety-five percent of the population of employees has a systolic blood pressure between 122 and 138.
(c) If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the
population mean systolic blood pressure.
(d) The probability that the population mean blood pressure is between 122 and 138 is .95.
(e) If the procedure were repeated many times, 95% of the sample means would be between 122 and 138.
6) A statistical study has a null hypothesis that the mean recovery time for a cut (the time it takes for the scab to
fall off) is 7 days. Which of the following could be the alternative hypothesis?
(a)
(b)
(c)
(d)
The mean recovery time is greater than or equal to 7 days.
The mean recovery time is less than or equal to 7 days.
The mean recovery time is not equal to 7 days.
All of the above.
7) A null hypothesis that the mean height of females is 64 in. is to be tested at the 1% significance level against
an alternative hypothesis that the mean height of females is not 64 in. The 99% confidence interval for the
sample mean is 61 to 67. From this information, the null hypothesis:
(a)
(b)
(c)
(d)
should be rejected at the 1% significance level.
should not be rejected at the 1% significance level.
should be rejected at the 5% significance level.
none of these.
8) A machine is supposed to fill bags with 8 pounds of salt. To test if this machine is working properly, the
weights of 30 randomly selected bags is measured. A 95% confidence interval runs from 8.5 to 9.1. From
this information, it may be concluded:
(a)
(b)
(c)
(d)
there is a statistically significant difference between the sample mean and 8 pounds.
there is not a statistically significant difference between the sample mean and 8 pounds.
the sample mean is exactly equal to 8 pounds.
none of these.
9) A significance test gives a P-value of 0.04. From this we can
(a) Reject H0 at the 1% significance level
(b) Reject H0 at the 5% significance level
(c) Say that the probability that H0 is false is 0.04
(d) Say that the probability that H0 is true is 0.04
(e) None of the above.
10) In general, the width of a confidence interval for a mean
(a) will be wider for a 95% confidence interval than for a 99% confidence interval.
(b) will be wider for a sample size 25 than for a sample size 100.
(c) will be wider for a sample size of 100 than for a sample size 25.
11)
It is believed that the average amount of money spent per U.S. household per week on food is about $98,
with standard deviation $10. A random sample of 100 households in a certain affluent community yields a
mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all
households in this community is higher than the national average.
(a) Perform a significance test at the   0.05 significance level. (State the type of test, null and alternative
hypotheses, conditions, show your calculations and sketch, and state your conclusion in context.)
(b) Describe a Type I error in the context of this problem. What is the probability of making a Type I error?
(c) Describe a Type II error in the context of this problem. Give two ways to reduce the probability of a
Type II error.
12) A steel mill’s milling machine produces steel rods that are supposed to be 5 cm in diameter. When the
machine is in statistical control, the rod diameters vary according to a normal distribution with mean µ =
5 cm and standard deviation  = 0.02 cm. A large sample of 150 produced by the machine yields a
sample mean diameter of 5.005 cm.
(a) Construct a 99% confidence interval for the true mean diameter of the rods produced by the milling
machine. (Show your conditions, calculations, and write your conclusions in context.)
(b) Does the interval in (a) give you reason to suspect that the machine is not producing rods of the correct
diameter? State appropriate hypotheses and a significance level. Then explain your conclusion.