MT3

txt

School

University of Saskatchewan *

*We aren’t endorsed by this school

Course

245

Subject

Economics

Date

Jan 9, 2024

Type

txt

Pages

Uploaded by DeanSkunk2287

1. A random sample of n = 49 observations has a mean x = 26.3 and a standard deviation s = 3.4. (a) Give the point estimate of the population mean . ? Find the 95% margin of error for your estimate. (Round your answer to four decimal places.) (b) Find a 90% confidence interval for . (Round your answers to three decimal ? places.) ___ to ___ What does "90% confident" mean? In repeated sampling, 10% of all intervals constructed in this manner will ? enclose the population mean. There is a 10% chance that an individual sample mean will fall within the ? interval limits. There is a 90% chance that an individual sample mean will fall within the ? interval. 90% of all values will fall within the interval limits. ? In repeated sampling, 90% of all intervals constructed in this manner will ? enclose the population mean. (c) Find a 90% lower confidence bound for the population mean . (Round your answer ? to two decimal places.) Why is this bound different from the lower confidence limit in part (b)? This bound is calculated using , while the lower confidence limit in part (b) ? z? is calculated using /2. z? This bound is calculated using sqrt(n), while the lower confidence limit in ? part (b) is calculated using n. This bound is calculated using /2, while the lower confidence limit in part ? z? (b) is calculated using . z? The lower bounds are based on different values of x. ? This bound is calculated using n, while the lower confidence limit in part (b) ? is calculated using sqrt(n). (d) How many observations do you need to estimate to within 0.5, with probability ? equal to 0.95? (Round your answer up to the nearest whole number.) 2. A random sample of n = 500 observations from a binomial population produced x = 110 successes. (a) Find a point estimate for p. Find the 95% margin of error for your estimator. (Round your answer to three decimal places.) (b) Find a 90% confidence interval for p. (Round your answers to three decimal places.) Interpret this interval. In repeated sampling, 90% of all intervals constructed in this manner will ? enclose the population proportion. There is a 90% chance that an individual sample proportion will fall within the ? interval. There is a 10% chance that an individual sample proportion will fall within the ? interval. In repeated sampling, 10% of all intervals constructed in this manner will ? enclose the population proportion. 90% of all values will fall within the interval. ?

3. Independent random samples were selected from binomial populations 1 and 2. Suppose you wish to estimate (p1 − p2) correct to within 0.02, with probability equal to 0.99, and you plan to use equal sample sizes—that is, n1 = n2. How large should n1 and n2 be? (Assume maximum variation. Round your answer up to the nearest whole number.) n1 = n2 = 4. Acid rain, caused by the reaction of certain air pollutants with rainwater, is a growing problem in the United States. Pure rain falling through clean air registers a pH value of 5.7 (pH is a measure of acidity: 0 is acid; 14 is alkaline). A sample of n = 50 rainfalls produced pH readings with x = 3.6 and s = 0.6. Do the data provide sufficient evidence to indicate that the mean pH for rainfalls is more acidic (Ha: < 5.7 pH) than pure rainwater? Test using = 0.05. Note that this ? ? inference is appropriate only for the area in which the rainwater specimens were collected. State the null and alternative hypotheses. H0: = 5.7 versus Ha: > 5.7 ? ? ? H0: > 5.7 versus Ha: < 5.7 ? ? ? H0: < 5.7 versus Ha: = 5.7 ? ? ? H0: ≠ 5.7 versus Ha: < 5.7 ? ? ? H0: = 5.7 versus Ha: < 5.7 ? ? ? Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) test statistic z = rejection region z > z < State your conclusion. H0 is rejected. There is sufficient evidence to indicate that the average pH ? for rainfalls is more acidic than pure rainwater. H0 is not rejected. There is sufficient evidence to indicate that the average ? pH for rainfalls is more acidic than pure rainwater. H0 is rejected. There is insufficient evidence to indicate that the average pH ? for rainfalls is more acidic than pure rainwater. H0 is not rejected. There is insufficient evidence to indicate that the average ? pH for rainfalls is more acidic than pure rainwater. 5. In a study to assess various effects of using a female model in automobile advertising, 100 men were shown photographs of two automobiles matched for price, colour, and size, but of different makes. One of the automobiles was shown with a female model to n1 = 50 of the men (group A), and both automobiles were shown without the model to the other n2 = 50 men (group B). In group A, the automobile shown with the model was judged as more expensive by x1 = 35 men; in group B, the same automobile was judged as the more expensive by x2 = 26 men. Do these results indicate that using a female model increases the perceived cost of an automobile? Use a one-tailed test with = 0.05. (Round your answers to two decimal places.) ? (1-2) Null and alternative hypotheses: H0: (p1 − p2) ≠ 0 versus Ha: (p1 − p2) = 0 ? H0: (p1 − p2) = 0 versus Ha: (p1 − p2) ≠ 0 ? H0: (p1 − p2) = 0 versus Ha: (p1 − p2) < 0 ? H0: (p1 − p2) = 0 versus Ha: (p1 − p2) > 0 ? H0: (p1 − p2) < 0 versus Ha: (p1 − p2) > 0 ? (3) Test statistic: z =

(4) Rejection region: If the test is one-tailed, enter NONE for the unused region. z > z < (5) Conclusion: H0 is rejected. There is insufficient evidence to indicate that using a female ? model increases the perceived cost of an automobile. H0 is not rejected. There is insufficient evidence to indicate that using a ? female model increases the perceived cost of an automobile. H0 is not rejected. There is sufficient evidence to indicate that using a ? female model increases the perceived cost of an automobile. H0 is rejected. There is sufficient evidence to indicate that using a female ? model increases the perceived cost of an automobile. 6. A random sample of n = 15 observations from a normal population produced x = 47.9 and s2 = 4.4. Test the hypothesis H0: = 48 against Ha: ≠ 48 at the 5% level ? ? of significance. State the test statistic. (Round your answer to three decimal places.) t = State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) t > t < State the conclusion. H0 is rejected. There is sufficient evidence to conclude that the mean ? different from 48. H0 is not rejected. There is sufficient evidence to conclude that the mean is ? different from 48. H0 is not rejected. There is insufficient evidence to conclude that the mean is ? different from 48. H0 is rejected. There is insufficient evidence to conclude that the mean is ? different from 48. 7. To test the effect of alcohol in increasing the reaction time to respond to a given stimulus, the reaction times of seven people were measured. After consuming 89 mL of 40% alcohol, the reaction time for each of the seven people was measured again. Do the following data indicate that the mean reaction time after consuming alcohol was greater than the mean reaction time before consuming alcohol? Use = ? 0.05. (Use before − after = d. Round your answers to three decimal places.) ? ? ? Table: Person | 1 | 2 | 3 | 4 | 5 | 6 | 7 Before | 3 | 5 | 4 | 3 | 2 | 6 | 2 After | 7 | 8 | 2 | 5 | 3 | 5 | 4 (1-2) Null and alternative hypotheses: H0: d = 0 versus d ≠ 0 ? ? ? H0: d = 0 versus d > 0 ? ? ? H0: d ≠ 0 versus d = 0 ? ? ? H0: d < 0 versus d > 0 ? ? ? H0: d = 0 versus d < 0 ? ? ? (3) Test statistic: t = (4) Rejection region: If the test is one-tailed, enter NONE for the unused region.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

t > t < (5) Conclusion: H0 is not rejected. There is sufficient evidence to indicate that the mean ? reaction time is greater after consuming alcohol. H0 is rejected. There is insufficient evidence to indicate that the mean ? reaction time is greater after consuming alcohol. H0 is not rejected. There is insufficient evidence to indicate that the mean ? reaction time is greater after consuming alcohol. H0 is rejected. There is sufficient evidence to indicate that the mean reaction ? time is greater after consuming alcohol. 8. At a time when energy conservation is so important, some scientists think closer scrutiny should be given to the cost (in energy) of producing various forms of food. Suppose you wish to compare the mean amount of oil required to produce 4047 square metres of corn versus 4047 m^2 of cauliflower. The readings (in barrels of oil per 4047 m^2), based on 80,937 m^2 plots, seven for each crop, are shown in the table. Corn Cauliflower 5.5 15.7 7.0 13.6 4.6 17.8 6.0 16.7 7.8 15.9 4.6 16.5 5.9 17.2 Use these data to find a 90% confidence interval for the difference between the mean amounts of oil required to produce these two crops. (Round your answers to three decimal places.) ___ to ___ barrels of oil per square metre

Related Documents

math assessment.docx

FINCB 571_Final Reflection.docx

International Management Assignment.docx

Component-6.docx

FNH 355 Assignment A.2 .pdf

BIOL-Discussion Assignment Unit 66.docx

Price Elasticity Calculations.docx

Data Files (Project 4).xlsx

ECO4000 - REVIEW word.docx

Discussion Forum Unit 5--PHILL.docx

ECO 4000 Quizzes .docx

Post-lab 4 results.docx

Recommended textbooks for you

Managerial Economics: Applications, Strategies an...

Economics

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:Cengage Learning

Managerial Economics: A Problem Solving Approach

Economics

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Cengage Learning

Microeconomic Theory

Economics

ISBN:9781337517942

Author:NICHOLSON

Publisher:Cengage

MACROECONOMICS FOR TODAY

Economics

ISBN:9781337613057

Author:Tucker

Publisher:CENGAGE L

Micro Economics For Today

Economics

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Cengage,

Economics For Today

Economics

ISBN:9781337613040

Author:Tucker

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

Recommended textbooks for you

Managerial Economics: Applications, Strategies an...
Economics
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Microeconomic Theory
Economics
ISBN:9781337517942
Author:NICHOLSON
Publisher:Cengage
MACROECONOMICS FOR TODAY
Economics
ISBN:9781337613057
Author:Tucker
Publisher:CENGAGE L
Micro Economics For Today
Economics
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Cengage,
Economics For Today
Economics
ISBN:9781337613040
Author:Tucker
Publisher:Cengage Learning