Download C.10 Review Sheets - Mrs. McDonald

Name:
C.10 Review B & C
AP Stats
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1.
The value of z* required for a 70% confidence interval is
(a) -0.5244
(b) 1.036
(c) 0.5244
(d) 0.6179
(e) The answer can’t be determined from the information given.
(f) None of the above. The answer is _____________________.
2.
A significance test allows you to reject a hypothesis H0 in favor of an alternative Ha at the 5% level of significance. What can you
say about significance at the 1% level?
(a) H0 can be rejected at the 1% level of significance.
(b) There is insufficient evidence to reject H0 at the 1% level of significance.
(c) There is sufficient evidence to accept H0 at the 1% level of significance.
(d) Ha can be rejected at the 1% level of significance.
(e) The answer can’t be determined from the information given.
3.
A 95% confidence interval for the mean  of a population is computed from a random sample and found to be 9 ± 3. We may
conclude that
(a) There is a 95% probability that  is between 6 and 12.
(b) There is a 95% probability that the true mean is 9 and a 95% chance the true margin of error is 3.
(c) If we took many, many additional random samples and from each computed a 95% confidence interval for  , approximately
95% of these intervals would contain  .
(d) If we took many, many additional random samples and from each computed a 95% confidence interval for  , 95% of them
would cover the values from 6 to 12.
(e) All of the above.
4.
A 95% confidence interval for the mean reading achievement score for a population of third grade students is (44.2, 54.2).
Suppose you compute a 99% confidence interval using the same information. Which of the following statements is correct?
(a) The intervals have the same width.
(b) The 99% interval is shorter.
(c) The 99% interval is longer.
(d) The answer can’t be determined from the information given.
(e) None of the above. The answer is ______________________.
5.
Which of the following are correct?
I. The power of a significance test depends on the alternative value of the parameter.
II. The probability of a Type II error is equal to the significance level of the test.
III. Type I and Type II errors only make sense when a significance level has been chosen in
(a) I and II only
(b) I and III only
(c) II and III only
(d) I, II, and III
(e) None of the above gives the complete set of true responses.
6.
In a test of H0: µ = 100 against Ha: µ
the test is thus equal to:
(a)
(b)
(c)
(d)
(e)

100, a sample of size 80 produces z = 0.8 for the value of the test statistic. The P-value of
0.20
0.40
0.29
0.42
0.21
Chapter 10
advance.
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7.
To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n
times and the mean x of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean 
and standard deviation
 = 0.01 g. How large should n be so that a 95% confidence interval for
(a) 100
(b) 196
(c) 27061
(d) 10000
(e) 38416
8.

has a margin of error of ± 0.0001?
A 95% confidence interval for µ is calculated to be (1.7, 3.5). It is now decided to test the hypothesis H 0: µ = 0 vs. Ha: µ
 = 0.05 level, using the same data as was used to construct the confidence interval.
(a)
(b)
(c)
(d)
(e)

0 at the
We cannot test the hypothesis without the original data.
We cannot test the hypothesis at the = 0.05 level since the  = 0.05 test is connected to the 97.5% confidence interval.
We can only make the connection between hypothesis tests and confidence intervals if the sample sizes are large.
We would reject H0 at level  = 0.05.
We would accept H0 at level  = 0.05.
Part 2: Free Response
Communicate your thinking clearly and completely.
9.
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
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. Follow the
inference toolbox.
(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.
(c) Describe a Type II error in the context of this problem. How could the manufacturer decrease the probability of a Type II error.
10. A pharmaceutical manufacturer does a chemical analysis to check the potency of products. The standard release potency for
cephalothin crystals is 910. An assay of 16 lots gives the following potency data:
897
914
913
906
916
918
905
921
918
906
895
893
908
906
907
901
Assume a population standard deviation  = 8.2.
(a) Construct a 99% confidence interval for the population mean. Follow the Inference Toolbox.
You want to test hypotheses about the mean population potency,
H0:
Ha:
µ = 910
µ < 910
at the 1% level of significance. The z test statistic is z =
(b) What is the rule for rejecting
(c) What values of
x
H0
x  910 8.2
16
.
in terms of z?
would lead you to reject
H0?
(d) Describe a Type I error in the context of this problem. What is the probability of a Type I error?
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Directions: Work on these sheets. Answer completely, but be concise. A normal probability table is attached.
1.
2.
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%.
A certain population follows a normal distribution with mean
 = 2.5. You collect data and test the hypotheses
H0: 
= 1,
Ha:  

and standard deviation
1.
You obtain a P-value of 0.022. Which of the following is true?
(a) 95% confidence interval for  will include the value 1.
(b) A 95% confidence interval for  will include the value 0.
(c) A 99% confidence interval for  will include the value 1.
(d) A 99% confidence interval for  will include the value 0.
(e) None of these is necessarily true.
3.
The government claims that students earn an average of $4500 during their summer break from studies. A random sample of
students gave a sample average of $3975 and a 95% confidence interval was found to be $3525 < µ < $4425. This interval is
interpreted to mean that:
(a) If the study were to be repeated many times, there is a 95% probability that the true average summer earnings is not $4500 as
the government claims.
(b) Because our specific confidence interval does not contain the value $4500 there is a 95% probability that the true average
summer earnings is not $4500.
(c) If we were to repeat our survey many times, then about 95% of all the confidence intervals will contain the value $4500.
(d) If we repeat our survey many times, then about 95% of our confidence intervals will contain the true value of the average
earnings of students.
(e) There is a 95% probability that the true average earnings are between $3525 and $4425 for all students.
4.
In a statistical test for the equality of a mean, such as H0 µ = 10, if  = 0.05,
(a)
(b)
(c)
(d)
(e)
95% of the time we will make an incorrect inference
5% of the time we will say that there is a real difference when there is no difference
5% of the time we will say that there is no real difference when there is a difference
95% of the time the null hypothesis will be correct
5% of the time we will make a correct inference
5.
I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the mean
of the population. Which of the following would produce a new confidence interval with larger width (larger margin of error) based
on these same data?
(a) Use a larger confidence level.
(b) Use a smaller confidence level.
(c) Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger.
(d) Increase the sample size.
(e) Nothing can guarantee absolutely that you will get a larger interval. One can only say the chance of obtaining a larger interval
is 0.05.
6.
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.
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7.
Consider the following graph of the mean yield of barley in 1980, 1984, and 1988 along with a 95% confidence interval.
Which of the following is INCORRECT?
(a) Since the confidence intervals for 1984 and 1980 have considerable overlap, there is little evidence that the sample means
differ.
(b) Since the confidence intervals for 1988 and 1980 do not overlap, there is good evidence that their respective population
means differ.
(c) The sample mean for 1984 is about 195 g/400m2.
(d) The sample mean for 1988 is less than the sample mean for 1984.
(e) The estimate of the population mean in 1988 is more precise than that for 1980 since the confidence interval for 1988 is
narrower than that for 1980.
Part 2: Free Response
Communicate your thinking clearly and completely.
8.
Patients with chronic kidney failure may be treated by dialysis, using a machine that removes toxic wastes from the blood, a
function normally performed by the kidneys. Kidney failure and dialysis can cause other changes, such as retention of
phosphorous, that must be corrected by changes in diet. A study of the nutrition of dialysis patients measured the level of
phosphorous in the blood of several patients on six occasions. Here are the data for one patient (milligrams of phosphorous per
deciliter of blood):
5.6
5.3
4.6
4.8
5.7
6.4
The measurements are separated in time and can be considered an SRS of the patient’s blood
phosphorous level. Assume that this level varies normally with  = 0.9 mg/dl. The normal range of phosphorous in the blood is
considered to be 2.6 to 4.8 mg/dl.
(a)
Is there strong evidence that the patient has a mean phosphorous level that exceeds 4.8? Follow the Inference Toolbox.
9.
(b)
Describe a Type I error and a Type II error in this situation. Which is more serious?
(c)
Give two ways to increase the power of the test you performed in (a).
You measure the weights of 24 male runners. You do not actually choose an SRS, but you are willing to assume that these runners
are a random sample from the population of male runners in your town or city. Here are their weights in kilograms:
67.8
61.9
63.0
53.1
62.3
59.7
55.4
58.9
60.9
69.2
63.7
68.3
64.7
65.6
56.0
57.8
66.0
62.9
53.6
65.0
55.8
60.4
69.3
61.7
Suppose that the standard deviation of the population is known to be  = 4.5 kg.
(a) Construct a 95% confidence interval for
Toolbox.
 , the mean of the population from which the sample is drawn. Follow the Inference
(b) Explain the meaning of 95% confidence in part (a).
(c) Based on this confidence interval, does a test of
H 0 :   61.3 kg
H a :   61.3 kg
reject H 0 at the 5% significance level? Justify your answer.
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