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Unformatted text preview: Test 11B AP Statistics Name: Directions: Work on these sheets. Tables and formulas appear on a separate sheet. Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. You want to compute a 90% conﬁdence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of t* you would use for this
interval is (a) 1.96 (b) 1.645 (c) 1.699 (d) .90 (e) 1.311 (f) None of the above 2. A 95% conﬁdence interval for the mean reading achievement score for a population of thirdgrade
students is (44.2, 54.2). The margin of error of this interval is
(a) 95%
(b) 5
(c) 2.5
(d) 10
(e) The answer cannot be determined from the information given. 3. The effect of acid rain upon the yield of crops is of concern in many places. In order to determine baseline yields, a sample of 13 ﬁelds was selected, and the yield of barley (g/400m2)
was determined. The output from SAS appears below: QUANTILES(DEF=4) EXTREMES
N 13 SUM WGTS 13 100% MAX 392 99% 392 LOW HIGH
MEAN 220.231 SUM 2863 75% Q3 234 95% 392 161 225
STD DEV 58.5721 VAR 3430.69 50% MED 221 90% 330 168 232
SKEW 2.21591 KURT 6.61979 25% Q1 174 10% 163 169 236
USS 671689 CSS 41168.3 0% MIN 161 5% 161 179 239
CV 26.5958 STD MEAN 16.245 1% 161 . 205 392 A 95% conﬁdence interval for the mean yield is:
(a) 220.2 d: 1.96(58.6)
(b) 220.2 i 1.96(16.2)
(c) 220.2 i: 2.18(58.6)
(d) 220.2 1 2.18(16.2)
(e) 220.2 :1: 2.16(16.2) 4. To use the twosample t procedure to perform a signiﬁcance test on the difference between two
means, we assume
(a) The populations’ standard deviations are known
(b) The samples from each population are independent
(c) The distributions are exactly normal in each population
(d) The sample sizes are large
(e) All of the above Chapter 11 1 Test 11B 5. We wish to test if a new feed increases the mean weight gain compared to an old feed. At the
conclusion of the experiment it was found that the new feed gave a 10 kg bigger gain than the
old feed. A twosample ttest with the proper onesided alternative was done and the resulting
P—Value was 0.082. This means: (a) There is an 8.2% chance the null hypothesis is true. (b) There was only a 8.2% chance of observing an increase greater than 10 kg (assuming the
null hypothesis was true). (c) There was only an 8.2% chance of observing an increase greater than 10 kg (assuming the
null hypothesis was false). (d) There is an 8.2% chance the alternate hypothesis is true. (e) There is only an 8.2% chance of getting a 10 kg. increase. 6. The water diet requires one to drink two cups of water every half hour from when one gets up until
one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to
test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The
weights (in pounds) are Person 1 2 3 4
Weight before the diet 180 125 240 150
Weight after six weeks 170 130 215 152 For the population of all adults, assume that the weight loss after six weeks on the diet (weight
before beginning the diet — weight after six weeks on the diet) is normally distributed with mean ,u.
To determine if the diet leads to weight loss, we test the hypotheses Hoztt=0,Ha:/.t>0. Based on these data we conclude that (a) We would not reject H0 at signiﬁcance level 0.10. (b) We would reject H0 at signiﬁcance level 0.10 but not at 0.05.
(c) We would reject H0 at signiﬁcance level 0.05 but not at 0.01.
(d) We would reject H0 at signiﬁcance level 0.01. (e) The sample size is too small to allow use of the tprocedures. Chapter 11 2 Test 11B Part 2: Free Response
Answer completely, but be concise. Write sequentially and show all steps. 7. The level of dissolved oxygen in a river is an important indicator of the water’s ability to support aquatic life. You collect water samples at 15 randomly chosen locations along a stream
and measure the dissolved oxygen. Here are your results in milligrams per liter: 4.53, 5.04, 3.29, 5.23, 4.13, 5.50, 4.83, 4.40, 5.42, 6.38, 4.01, 4.66, 2.87, 5.73, 5.55 Construct a 95% conﬁdence interval for the mean dissolved oxygen level for this stream. Follow
the Inference Toolbox. In a study of the effectiveness of weightloss programs, 47 subjects who were at least 20% overweight
took part in a group support program for 10 weeks. Private weighings determined each subject’s
weight at the beginning of the program and 6 months after the program’s end. The matched pairs t test was used to assess the signiﬁcance of the average weight loss. The paper reporting the study said,
“The subjects lost a signiﬁcant amount of weight over time, t(46) = 4.68, P < 0.01.” 8. Why was the matchedpairs t statistic appropriate? 9. Explain to someone who knows no statistics but is interested in weightloss programs what the
practical conclusion is. Chapter 11 3 Test 11B 10. The paper follows the tradition of reporting signiﬁcance only at ﬁxed levels such as a = 0.01. In fact the results are more signiﬁcant than “P < 0.01” suggests. What can you say about the Pvalue
of the t test? A study of iron deﬁciency among infants compared samples of infants following different feeding
regimens. One group contained breastfed infants, while the children in another group were fed a standard baby formula without any iron supplements. Here are the results on blood hemoglobin levels
at 12 months of age. Group :1 7C 3
Breast—fed 23 13.3 1.7
Formula 19 12 .4 l. 8 11. Is there signiﬁcant evidence that the mean hemoglobin level is higher among breastfed babies?
Give appropriate statistical evidence to support your conclusion. 12. Construct a 95% conﬁdence interval for the mean difference in hemoglobin level between the two
populations of infants. Interpret your interval in the context of this problem. I pledge that I have neither given nor received aid on this test. Chapter 1] y 4 Test 11B (0.61. {lessees (a); db) SH), ‘iibgpﬂbl 6 ts”) Part 2: Free Response
Answer completely, but be concise. Write sequentially and show all steps. 7. The level of dissolved oxygen in a river is an important indicator of the water’s ability to
support aquatic life. You collect water samples at 15 randomly chosen locations along a stream
and measure the dissolved oxygen. Here are your results in milligrams per liter: 4.53, 5.04, 3.29, 5.23, 4.13, 5.50, 4.83, 4.40, 5.42, 6.38, 4.01, 4.66, 2.87, 5.73, 5.55 Construct a 95% conﬁdence interval for the mean dissolved oxygen level for this stream. Follow
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regimens. One group contained breast—fed infants, while the children in another group were fed a standard baby formula without any iron supplements. Here are the results on blood hemoglobin levels
at 12 months of age. Group n 35 s
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populations of infants. Interpret your interval in the context of this problem. /\TK arm, weoeme wreckth 150a “(ll/Q Mew Vrﬁeeteweﬁ: ,M
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 Spring '11
 Smith
 Statistics

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