## Stat 215 A Fast Food Restaurant Estimates That The Mean

StatisticsAysha RossLab Chapter 7 and 8(Confidence Intervals are from Chapter 6 but are incorporated here)Write the null and alternative in terms of the appropriate parameter(ex. H0: µ=10). Clearly identify all pieces requested. Based on what isasked you will need to decide if you are using a one sample or twosample test about the mean large samples or small samples, proportion,or standard deviation. 1. A fast food restaurant estimates that the mean sodium content in one of itsbreakfast sandwiches is no more than 920 milligrams. A random sample of 44breakfast sandwiches has a mean sodium content of 925 with a standarddeviation of 18 milligrams. At ? = 0. 10, do you have enough evidence toreject the restaurant’s claim?a. Null hypothesis: H0: µ ? 920b. Alternative hypothesis: H0: µ >, 920c. Test statistic: d. Critical value(s) and region(s), sketch the distribution: e. P-value: f. The 90% confidence interval: g. Conclusion: State whether you are accepting or rejecting the null. ALSOTO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION. BEING “WORDY” IS O. K. Fail to reject/reject the null hypotheses because the p-vale is greater than/less than theh. Based on whether you failed to reject the null hypothesis or rejected thenull hypothesis, what type of error might have been committed, a Type Ierror or a Type II error? Explain. A type ½ error might have been committed because2. A polling agency claims that over 40% of adults shop for a gift within a weekof an event. In a random survey of 2730 people in the United States, 1130said they shop for a gift within a week on an event. Test the agency’s claim atthe ? = 0. 10 level. What can you conclude?a. Null hypothesis: H0: µ ? 40b. Alternative hypothesis: H0: µ >, 40c. Test statistic: d. Critical value(s) and region(s), sketch the distribution: e. P-value: f. The 90% confidence interval: g. Conclusion: State whether you are accepting or rejecting the null. ALSOTO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION. BEING “WORDY” IS O. K. h. In this problem, the normal distribution was used as an approximation tothe binomial. Show that the conditions were met to use the normaldistribution. 3. For this problem, you will use the confidence interval to make a decision andanswer the question. In a study of the effects of prenatal cocaine use oninfants, the following sample data were obtained for weights at birth: n = 190,x 2700 g, s = 645g (based on data from “Cognitive Outcomes of PreschoolChildren With Prenatal Cocaine Exposure” by Singer, et al, Journal of theAmerican Medical Association, Vol. 291, No. 20). It is known that the meanweight for babies born to mothers who do not use cocaine is 3103g. Is thereconvincing evidence to conclude that birth weights are affected by cocaineuse?a. Construct a 99% confidence interval: b. Does the confidence interval contain the value 3103g, the mean weight forbabies born to mothers who do not use cocaine?Based on the confidence interval, is there convincing evidence to concludethat birth weights are affected by cocaine use? Explain your answer: 4. Does the growth of trees vary more when the trees are young? TheInternational Tree Ring Data Base collected data on a particular 440-year-oldDouglas fir tree (C. J. Earle, L. B. Brubaker, and G. Segura, International TreeRing Data Base, NOAA/NGDC Paleoclimatology Program, Boulder, CO). The standard deviation of the annual ring growth in the tree’s first 80 years oflife was 0. 8 millimeters per year. We are interested in testing whether thepopulation standard deviation of annual ring growth in the tree’s later years isless than 0. 8mm per year. The sample variance for a random sample of size101 taken from the tree’s later years is s2 = 0. 3136. Assume a level ofsignificance of 0. 05. a. Null hypothesis: b. Alternative hypothesis: c. Test statistic: d. Critical value(s) and region(s), sketch the distribution: e. P-value (you will have to use StatCrunch or Minitab to get this): f. The 95% confidence interval: g. Conclusion: State whether you are accepting or rejecting the null. ALSOTO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION. BEING “WORDY” IS O. K. h. Based on whether you failed to reject the null hypothesis or rejected thenull hypothesis, what type of error might have been committed, a Type Ierror or a Type II error? Explain. Lab Chapter 8Perform a hypothesis test for the following problems. Clearly identify the parameters inthe hypotheses. You don’t have to find the confidence intervals, although they are easilyobtained using technology. 1. In 2013, 74 recent graduates of Farmington High School took the Accuplacer atSan Juan College and 43 of those graduates placed into developmental math. Forthe same year, 74 recent graduates of Piedra Vista High School took theAccuplacer at San Juan College and 58 of those graduates placed intodevelopmental math (San Juan College Office of Institutional Research, July2014). At a level of significance of 0. 05, test the claim that the proportion ofgraduates that placed into developmental math was higher for Piedra Vista HighSchool graduates than for Farmington High School graduates. i. Null hypothesis: j. Alternative hypothesis: k. Test statistic: l. Critical value(s) and region(s), sketch the distribution: m. P-value: n. Conclusion: State whether you are accepting or rejecting the null. ALSOTO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION. BEING “WORDY” IS O. K. o. In this problem, the samples need to be large enough to use a normalsampling distribution. You will need to pool the proportions as shown insection 8-4. Show these conditions are met. 2. Many studies have been conducted to test the effects of marijuana use on mentalabilities. In one such study, groups of light and heavy users of marijuana incollege were tested for memory recall, with the results given below (based on datafrom “The Residual Cognitive Effects of heavy marijuana Use in CollegeStudents” by Pope and Yurgelun-Todd, journal of the American MedicalAssociation, Vol. 275, No. 7). Use a 0. 01 significance level to test the claim thatthe population of heavy marijuana users has a lower mean than the light users. Items sorted correctly by light marijuana users: n 64 , x 53. 3 , s 3. 6Items sorted correctly by heavy marijuana users: n 65 , x 51. 3 , s 4. 5a. Null hypothesis: b. Alternative hypothesis: c. Test statistic: d. Critical value(s) and region(s), sketch the distribution: e. P-value: f. Conclusion: State whether you are accepting or rejecting the null. ALSOTO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION. BEING “WORDY” IS O. K. g. Based on whether you failed to reject the null hypothesis or rejected thenull hypothesis, what type of error might have been committed, a Type Ierror or a Type II error? Explain. 3. The following table lists SAT scores before and after a sample of 10 students tooka preparatory course: StudentSAT scorebeforecourse (x)Sat scoreaftercourse (y)A700B840C830D860E840F690G830H1180I930J107072084082090087070080012009501080Is there sufficient evidence to conclude that the preparatory course is effective inraising test scores? Use a 0. 05 significance level. a. Null hypothesis: b. Alternative hypothesis: c. Test statistic: d. Critical value(s) and region(s), sketch the distribution: e. P-value: f. Conclusion: State whether you are accepting or rejecting the null. ALSO TOBE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION. BEING“WORDY” IS O. K. g. Based on whether you failed to reject the null hypothesis or rejected the nullhypothesis, what type of error might have been committed, a Type I error or aType II error? Explain. 4. An office furniture manufacturer installed a new adhesive application process andclaims that the new process has on average pounds of pressure that is greater thanthe old process. To compare the new process with the old process, randomsamples were selected from the two processes and “pull tests” were performed todetermine the number of pounds of pressure that were required to pull apart theglued parts. (This kind of test is an example of destructive testing. ) Let thefollowing be the data collected: Pounds of pressure needed for the new process: 1250 1210 990 1310 1320 1200 1290 1360 1120 1360 1310 1110 1320 980 950 1430 9601050 1310 1240 1420 1170 1470 1060Pounds of pressure needed for the old process: 1180 1360 1310 1190 920 1060 1440 1010 1310 980 1310 1030 960 800 1280 1080930 1050 1010 1310 940 860 1450 1070At ? = 0. 05, is there enough evidence to support the manufacturer’s claim?Assume the population variances are equal. a. Null hypothesis: b. Alternative hypothesis: c. Test statistic: d. Critical value(s) and region(s), sketch the distribution: e. P-value: f. Conclusion: State whether you are accepting or rejecting the null. ALSOTO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION. BEING “WORDY” IS O. K.

## STAT 215 A fast food restaurant estimates that the mean

Question

Statistics

Aysha Ross

Lab Chapter 7 and 8

(Confidence Intervals are from Chapter 6 but are incorporated here)

Write the null and alternative in terms of the appropriate parameter

(ex. H0: µ=10). Clearly identify all pieces requested. Based on what is

asked you will need to decide if you are using a one sample or two

sample test about the mean large samples or small samples, proportion,

or standard deviation.

1.

A fast food restaurant estimates that the mean sodium content in one of its

breakfast sandwiches is no more than 920 milligrams. A random sample of 44

breakfast sandwiches has a mean sodium content of 925 with a standard

deviation of 18 milligrams. At ? = 0.10, do you have enough evidence to

reject the restaurant’s claim?

a. Null hypothesis: H0: µ ? 920

b. Alternative hypothesis: H0: µ > 920

c. Test statistic:

d. Critical value(s) and region(s); sketch the distribution:

e. P-value:

f. The 90% confidence interval:

g. Conclusion: State whether you are accepting or rejecting the null. ALSO

TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.

BEING “WORDY” IS O.K.

Fail to reject/reject the null hypotheses because the p-vale is greater than/less than the

h. Based on whether you failed to reject the null hypothesis or rejected the

null hypothesis, what type of error might have been committed, a Type I

error or a Type II error? Explain.

A type ½ error might have been committed because

2.

A polling agency claims that over 40% of adults shop for a gift within a week

of an event. In a random survey of 2730 people in the United States, 1130

said they shop for a gift within a week on an event. Test the agency’s claim at

the ? = 0.10 level. What can you conclude?

a. Null hypothesis: H0: µ ? 40

b. Alternative hypothesis: H0: µ > 40

c. Test statistic:

d. Critical value(s) and region(s); sketch the distribution:

e. P-value:

f. The 90% confidence interval:

g. Conclusion: State whether you are accepting or rejecting the null. ALSO

TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.

BEING “WORDY” IS O.K.

h. In this problem, the normal distribution was used as an approximation to

the binomial. Show that the conditions were met to use the normal

distribution.

3.

For this problem, you will use the confidence interval to make a decision and

answer the question. In a study of the effects of prenatal cocaine use on

infants, the following sample data were obtained for weights at birth: n = 190,

x 2700 g, s = 645g (based on data from “Cognitive Outcomes of Preschool

Children With Prenatal Cocaine Exposure” by Singer, et al, Journal of the

American Medical Association, Vol. 291, No. 20). It is known that the mean

weight for babies born to mothers who do not use cocaine is 3103g. Is there

convincing evidence to conclude that birth weights are affected by cocaine

use?

a. Construct a 99% confidence interval:

b. Does the confidence interval contain the value 3103g, the mean weight for

babies born to mothers who do not use cocaine?

Based on the confidence interval, is there convincing evidence to conclude

that birth weights are affected by cocaine use? Explain your answer:

4.

Does the growth of trees vary more when the trees are young? The

International Tree Ring Data Base collected data on a particular 440-year-old

Douglas fir tree (C.J. Earle, L.B. Brubaker, and G. Segura, International Tree

Ring Data Base, NOAA/NGDC Paleoclimatology Program, Boulder, CO).

The standard deviation of the annual ring growth in the tree’s first 80 years of

life was 0.8 millimeters per year. We are interested in testing whether the

population standard deviation of annual ring growth in the tree’s later years is

less than 0.8mm per year. The sample variance for a random sample of size

101 taken from the tree’s later years is s2 = 0.3136. Assume a level of

significance of 0.05.

a. Null hypothesis:

b. Alternative hypothesis:

c. Test statistic:

d. Critical value(s) and region(s); sketch the distribution:

e. P-value (you will have to use StatCrunch or Minitab to get this):

f. The 95% confidence interval:

g. Conclusion: State whether you are accepting or rejecting the null. ALSO

TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.

BEING “WORDY” IS O.K.

h. Based on whether you failed to reject the null hypothesis or rejected the

null hypothesis, what type of error might have been committed, a Type I

error or a Type II error? Explain.

Lab Chapter 8

Perform a hypothesis test for the following problems. Clearly identify the parameters in

the hypotheses. You don’t have to find the confidence intervals, although they are easily

obtained using technology.

1. In 2013, 74 recent graduates of Farmington High School took the Accuplacer at

San Juan College and 43 of those graduates placed into developmental math. For

the same year, 74 recent graduates of Piedra Vista High School took the

Accuplacer at San Juan College and 58 of those graduates placed into

developmental math (San Juan College Office of Institutional Research, July

2014). At a level of significance of 0.05, test the claim that the proportion of

graduates that placed into developmental math was higher for Piedra Vista High

School graduates than for Farmington High School graduates.

i. Null hypothesis:

j. Alternative hypothesis:

k. Test statistic:

l. Critical value(s) and region(s); sketch the distribution:

m. P-value:

n. Conclusion: State whether you are accepting or rejecting the null. ALSO

TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.

BEING “WORDY” IS O.K.

o. In this problem, the samples need to be large enough to use a normal

sampling distribution. You will need to pool the proportions as shown in

section 8-4. Show these conditions are met.

2. Many studies have been conducted to test the effects of marijuana use on mental

abilities. In one such study, groups of light and heavy users of marijuana in

college were tested for memory recall, with the results given below (based on data

from “The Residual Cognitive Effects of heavy marijuana Use in College

Students” by Pope and Yurgelun-Todd, journal of the American Medical

Association, Vol. 275, No. 7). Use a 0.01 significance level to test the claim that

the population of heavy marijuana users has a lower mean than the light users.

Items sorted correctly by light marijuana users: n 64 , x 53.3 , s 3.6

Items sorted correctly by heavy marijuana users: n 65 , x 51.3 , s 4.5

a. Null hypothesis:

b. Alternative hypothesis:

c. Test statistic:

d. Critical value(s) and region(s); sketch the distribution:

e. P-value:

f. Conclusion: State whether you are accepting or rejecting the null. ALSO

TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.

BEING “WORDY” IS O.K.

g. Based on whether you failed to reject the null hypothesis or rejected the

null hypothesis, what type of error might have been committed, a Type I

error or a Type II error? Explain.

3. The following table lists SAT scores before and after a sample of 10 students took

a preparatory course:

Student

SAT score

before

course (x)

Sat score

after

course (y)

A

700

B

840

C

830

D

860

E

840

F

690

G

830

H

1180

I

930

J

1070

720

840

820

900

870

700

800

1200

950

1080

Is there sufficient evidence to conclude that the preparatory course is effective in

raising test scores? Use a 0.05 significance level.

a. Null hypothesis:

b. Alternative hypothesis:

c. Test statistic:

d. Critical value(s) and region(s); sketch the distribution:

e. P-value:

f. Conclusion: State whether you are accepting or rejecting the null. ALSO TO

BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION. BEING

“WORDY” IS O.K.

g. Based on whether you failed to reject the null hypothesis or rejected the null

hypothesis, what type of error might have been committed, a Type I error or a

Type II error? Explain.

4. An office furniture manufacturer installed a new adhesive application process and

claims that the new process has on average pounds of pressure that is greater than

the old process. To compare the new process with the old process, random

samples were selected from the two processes and “pull tests” were performed to

determine the number of pounds of pressure that were required to pull apart the

glued parts. (This kind of test is an example of destructive testing.) Let the

following be the data collected:

Pounds of pressure needed for the new process:

1250 1210 990 1310 1320 1200 1290 1360 1120 1360 1310 1110 1320 980 950 1430 960

1050 1310 1240 1420 1170 1470 1060

Pounds of pressure needed for the old process:

1180 1360 1310 1190 920 1060 1440 1010 1310 980 1310 1030 960 800 1280 1080

930 1050 1010 1310 940 860 1450 1070

At ? = 0.05, is there enough evidence to support the manufacturer’s claim?

Assume the population variances are equal.

a. Null hypothesis:

b. Alternative hypothesis:

c. Test statistic:

d. Critical value(s) and region(s); sketch the distribution:

e. P-value:

f. Conclusion: State whether you are accepting or rejecting the null. ALSO

TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.

BEING “WORDY” IS O.K.

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