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Unformatted text preview: MATH 2300 — Chapter 9 — Problems Express the null hypothesis.
1) Which could be the null hypothesis for the true proportion of fireﬂies unable to produce light?
A) H0: p a: 00012 HO: p = 00012 C) H0: p a 0.0012 D) H0: p < 0.0012 Examine the given statement, then identify whether the statement is a null hypothesis, an alternative hypothesis or
neither. 2) The mean income of workers who have majored in history is less than $25,000.
A) Null hypothesis B) Neither @Alternative hypothesis 3) The percentage of viewers tuned to FOX News is equal to 85%.
([9 Null hypothesis B) Neither C) Alternative hypothesis 4) The more college courses a person has, the higher their salary will be.
A) Alternative hypothesis B) Null hypothesis @Neither Determine the null and alternative hypotheses.
5) A manufacturer claims that the mean amount of cola in its 16 ounce bottles is 16.1 ounces. A consumer
advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. H0: p. = 16.1 ounces B) H0: p = 16.1 ounces
Ha: p s 16.1 ounces Ha: p > 16.1 ounces
C) H0: p. < 16.1 ounces H0: ti = 16.1 ounces
Ha: p > 16.1 ounces H341 < 16.1 ounces 6) A cereal company claims that the mean weight of it's individual serving boxes is at least 14 02.
A) H0: p: 14 B) H01p=14 C) H0: p: 14 H0: pt: 14 E) H0: p: 14
Ha:p¢14 Ha:p214 Hazp514 Hazp< 14 Hazp>14
AWNre»! <va 30"” {unison 00"“! 52 CD m E , clanLMG Luau you argue 7) The owner of a football team claims that the average attendance at games is over 81,000, and he is therefore
justified in moving the team to a city with a larger stadium. A) H0: pi = 81,000 B) H0: p. 2 81,000 C) H0: p = 81,000 (19 H0: i1 = 81,000 Ha: p. 2 81,000 H341 < 81,000 Ha: p 2 81,000 Ha: p. > 81,000 Select the most appropriate answer.
8) Which of the following would be an appropriate null hypothesis?
A) The population mean is not equal to 3.4. B) The sample mean is equal to 3.4.
@The population mean is equal to 3.4. D) The sample mean is greater than 3.4. 9) Which P—value provides the strongest evidence against the null hypothesis?
A) 0.05 B) 0.99 C) 1 D) —0.05 @0001 10) Which of the following statements is false?
A) The P—value is between 0 and 1.
B) The P—value represents the probability of obtaining the observed value or one even more extreme.
C) The smaller the Pvalue, the stronger the evidence is against H0. The P—value assumes Ha is true. 11) A researcher claims that less than 20% of American adults are allergic to pollen. In a random sample of 100
adults, 15% indicate that they have such an allergy. Calculate the test statistic z for the population proportion. vawss 3V  A ‘
0.: p: 02 :90 task sh’w c ~ Z, 95 v.
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1: 0'5620 M Find the P—value for the indicated hypothesis test.
13) A medical school claims that more than 28% of its students plan to go into general practice. It is found that
among a random sample of 130 of the schools students, 39% of them plan to go into general practice. Find the
PValue for testing the school's claim. A) 0.3078 B) 0.1635 C) 0.3461 0.0026 E) 00280
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24% 14) A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 100 such fax
machines, 5% are defective. Find the P—Value for testing the manufacturer's claim. A) 0.17 .34 C) 0.16 D) 0.33 E) 0.06
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_o.+2 o 15) Of 100 randomly selected subjects who followed a particular diet, 47 noticed an increase in their energy level.
Find the P~value for testing the claim that more than 50% of the people following a particular diet will ex erience increased energy.
.73 B) 0.23 C) 0.27 D) 0.50 E) 0.55
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(ob O. 72 9 7 P? nlM 3' 0,7 25 :2 : 0‘73 For the given sample data and null hypothesis, compute the value of the test statistic, z 16) A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include
1933 subjects with 30% saying that they play a sport. A) —35.90 B) 35.90 C) 17.59 47.59 E) 0.50 HO: P:o‘§ L25) Skohsswz % : €“9b ') sie, :IPOQ'PQ
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p: 05 .. O 0 H3 17) Out of 199 observations, 50% were successes. H0: p = 0.43. A) 1.29 1.99 C) 0.04 D) 1.72 E) 0.002
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P0: o4; State conclusion to signiﬁcance test in terms of the null hypothesis
18) A nationwide survey of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Can the value 065 be rejected if a survey of 490 homes in Omaha yields 336 with one or more lawn mowers? Use
a = 0.05. H0: p = 0.65. Ha: p > 0.65. Test statistic: z = 1.66. Pvalue: p = 0.0485.
State your coWrms of H0. W“ g
A) Reject Ha since the P—Value is less than a. )3 'VA‘M ‘ O 'Oq'XS < o . Ob : K ‘
B) Do not reject H0 since the Pvalue is less than a.
@eject H0 since the Pvalue is less than a.
D) Do not reject Ha since the P—value is less than a. Provide an appropriate response. 19) A study uses a random sample of size 9. The test statistic for testing H0: u = 12 versus Ha: u > 12 is t: 1.8. Find
‘ the a proximate PValue. W V) .1 a P’Vblu :3 005
B) 0.95 c1on d;aclow
C) 0.10 OH": W) .
D) 0.025 _. o i v 3
E) Cannot be determined without the sample standard deviation. State conclusion to significance test in terms of the null hypothesis
20) In a Quinnipiac University Poll of 1556 registered voters nationwide taken in June of 2007, 43% of those polled
blamed oil companies the most for the recent increase in gasoline prices. Test the claim that the mentage of
registered voters nationwide who blameﬂg‘ilcorrwipanies the most for the recent increase in gasolﬁi‘nehpﬂriﬂcesgat gagging, using (x2001. Test statistic: 22—159. P—Value=O.94 A) Since the Pvalue > a, we can conclude that the percentage of registered voters nationwide who blame oil
companies the most for the recent increase in gasoline prices is at least 45%.
B) Since the P~value is larger than 45%, we cannot conclude that the percentage of registered voters nationwide who blame oil companies the most for the recent increase in gasoline prices is at least 45%.
@ince the Pvalue > a, we cannot conclude that the percentage of registered voters nationwide who blame
oil companies the most for the recent increase in gasoline prices is at least 45%. D) Since the P—value > a, we conclude that the percentage of registered voters nationwide who blame oil
companies the most for the recent increase in gasoline prices is 43%. Ago/tum Ho: (3:452 5mm) gnaw = M4 > 0'0‘ : °"
HA5 P>4.§'/ ' "Do No), Y'eiack Ho i.,.,..«._c..,..w.__u.._~,. i~‘«£WWM Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic t.
21) Test the claim that for the population of female college students, the mean weight is given by p = 132 lb. Sample data are summarized as n = 20, it = 137 lb, and s = 14.2 leUse a signiﬁcance level of a = 0.1.
Find the test statistic t. 1.57 B) 1.729 C) 7.04 D) 14.2 E) —1.57 . : 0 A;
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7 x . siendavd. &,vi£«'\.)0m 22) Test the claim that the mean lifetime of a particular car engine is greater than 220,000 miles. Sample data are
summarized as n = 23, —x_2 226,450 miles, and s = 11,500 miles. Use a significance level of a = 0.01. Find the test statistic t. .
A) 12.9 B) 2.24 C) 224 .69 E) —2.69
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s : £5,500 Assume that a simple random sample has been selected from a normally distributed population. State the final conclusion.
23) Test the claim that for the population of female college students at a particular university, the mean weight is given by p. = 132 lb. Sample data are summarized as n z 20, ; = 137 lb, and s = 14.2 lb. Use a signiﬁcance level of
a 2 0.1.
H0 : p=132 P13442132
State your conclusion about H0.
A) t: 1.57, reject H0 B) 2 = 1.57, do not reject H0 @t = 1.57, do not reject H0 D) t = 1.57, do not reject H0 (“as 6p 10» 13 an exhumed oé (\LxL airframe“ @
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Yegecv) Ho. 24) Test the claim that the mean lifetime of a particular car engine is greater than 220,000 miles. Sample data are summarized as n = 23, ; = 226,450 miles, and s = 11,500 miles. Use a signiﬁcance level of a = 0.01.
H0: u = 220,000 Ha: p > 220,000 State your conclusion about H0.
A) t: ~2.69, reject H0 t = 2.69, reject H0 C) z = 2.69, reject H0 D) t: 12.9, reject H0 (M5 WWW 15 0* exiewiw 05 11M. CCU—lgibw @ g3 mix Sky's MC :rl“ 2433' 5mm, the (alchtaké
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:3) A.S,:23'(722. 2305 Select the most appropriate answer.
25) The test statistic for testing H0: p = 100 against Ha: u z 100 was t = 3.3, with P—Value 0.001. Which of the following is the appropriate conclusion?
ince the P—value is very small, we conclude that u a: 100.
) Since the P—value is very small, we are unable to conclude that u x 100.
C) In order to interpret the results, we must ﬁrst know the sample size.
D) Since the P—value is very small, we conclude that u = 100.
E) Since the P—Value is very small, we are unable to conclude that u = 100. (Alameuer 8M (Xx/AMI. is met) lire/e (30"9’olur "k {3 (“angina Vex/alum :ovool 4 0'05 =—* 0(
Mnbwu Regent Ho' 26) Failing to reject a false H0 B) has probability 1  E of occurring.
C) has probability a of occurring. @is a Type II error. H'o {5 (PALS £ 4
E) is a Type I error. A) is a correct decision. (“We 'Y
’i 27) Rejecting a true H0
A) has probability 1 — ii of occurring.
is a correct decision.
@is a Type I error.
D) has probability [3 of occurring.
E) is a Type II error. Classify the significance test as two—tailed, left—tailed, or right—tailed.
28) A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer
EQYQEE‘EXBIQBBXYEEE BREEZE} i§ﬁl§£ﬂt§g¢5t to detem‘ine Whether the mean 31110le less £11311 211118;.“
(A) Lefttailed B) Two—tailed C) Right—tailed D) None of these
0.1 /* = '6 "
Ha; f < Ib’ l 29) In the past, the mean lifetime for a certain type of ﬂashlight battery has been 9.3 hours. The manufacturer has
introduced a change in the production method and wants to perform a signiﬁcance test to determine whether Elle” mean lifetime has changed as a result.
A) Right—tailed B) Middletailed C) Left—tailed @Twotailed Ho 7“ 733
Mac/4 $9.2. 30) The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a
true mean temperature, p, of 46°F, ideal for a certain type of pilsner. The owner of the brewery does not agree
with the refrigerator manufacturer, and will conduct a signiﬁcme tem erature differs from this value.
Two—tailed B) Middle—tailed C) Right—tailed D) Lefttailed
‘ 0
Ho. ﬂ 2 46 P
Lu 1 /‘4 i 46 F For the given significance test, explain the meaning of a Type I error, a Type 11 error, or a correct decision as speciﬁed.
31) A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer
advocacy group wants to perform a significance test to determine whether the mean amount is actually less
than this. The hypotheses are:
H0: )1 = 16.1 ounces Ha: p< 16.1 ounces Explain the meaning of a Type I error.
A) Concluding that p. = 16.1 ounces when in fact p < 16.1 ounces
B) Failing to reject the hypothesis that p = 16.1 ounces when in fact it < 16.1 ounces
C) Concluding that p < 16.1 ounces when in fact p < 16.1 ounces
D Failing to reject the hypothesis that p = 16.1 ounces when in fact it = 16.1 ounces
@Concluding that p < 16.1 ounces when in fact p = 16.1 ounces riﬂe T QYTOV é Q1361“) Ho other.” Ho 33 “brute. Classify the conclusion of the significance test as a Type I error, a Type 11 error, or No error.
32) In the past, the mean lifetime for a certain type of flashlight battery has been 9.5 hours. The manufacturer has
introduced a change in the production method and wants to perform a signiﬁcance test to determine whether the mean lifetime has increased as a result. The hypotheses are: H0: 1.1 = 9.5 hours H341 > 9.5 hours Suppose that the resu‘l‘ts’gfihe samplelead to re‘ectio of he null h othesis. Classify that conclusion as a Type
I error, a Type 11 error, or a correct decisi, if in fact the mean runnin time has not increased. A) No error Type I error C) Type II error (has, \s (75%, ‘1 arm s‘mcc we “Fa HO 5AM“ “3 LS (\‘ruu. r ...
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This note was uploaded on 08/04/2011 for the course MATH 2300 taught by Professor Staff during the Spring '08 term at Texas Tech.
 Spring '08
 Staff
 Math, Statistics

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