Exam 12: Introduction to Statistical Inference: Testing Hypotheses About Single Means Z and T

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For inference about single means, df is

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The Director of Student Health Services wishes to know if her anti-smoking campaign has been effective. Last year, a complete survey of all students found the mean number of cigarettes smoked per day by students to be 8.6 with a standard deviation of 2.0. The Director of the Student Health Service obtains the following results from a recently selected random sample of students (in cigarettes smoked per day): The Director of Student Health Services wishes to know if her anti-smoking campaign has been effective. Last year, a complete survey of all students found the mean number of cigarettes smoked per day by students to be 8.6 with a standard deviation of 2.0. The Director of the Student Health Service obtains the following results from a recently selected random sample of students (in cigarettes smoked per day):      (a)Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions. (a)Set up The Director of Student Health Services wishes to know if her anti-smoking campaign has been effective. Last year, a complete survey of all students found the mean number of cigarettes smoked per day by students to be 8.6 with a standard deviation of 2.0. The Director of the Student Health Service obtains the following results from a recently selected random sample of students (in cigarettes smoked per day):      (a)Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions. and The Director of Student Health Services wishes to know if her anti-smoking campaign has been effective. Last year, a complete survey of all students found the mean number of cigarettes smoked per day by students to be 8.6 with a standard deviation of 2.0. The Director of the Student Health Service obtains the following results from a recently selected random sample of students (in cigarettes smoked per day):      (a)Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions. (b)Perform the statistical test ( The Director of Student Health Services wishes to know if her anti-smoking campaign has been effective. Last year, a complete survey of all students found the mean number of cigarettes smoked per day by students to be 8.6 with a standard deviation of 2.0. The Director of the Student Health Service obtains the following results from a recently selected random sample of students (in cigarettes smoked per day):      (a)Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions. (c)Draw final conclusions.

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(a) (a)     < 8.6 (b)      reject     (c) Conclude that the campaign was effective in reducing smoking among students.
< 8.6
(b)
(a)     < 8.6 (b)      reject     (c) Conclude that the campaign was effective in reducing smoking among students.
reject
(a)     < 8.6 (b)      reject     (c) Conclude that the campaign was effective in reducing smoking among students.
(c) Conclude that the campaign was effective in reducing smoking among students.

If If     and       and the critical values of z are       when       and       when       what would we do if our calculated value of z were -2.80? and If     and       and the critical values of z are       when       and       when       what would we do if our calculated value of z were -2.80? and the critical values of z are If     and       and the critical values of z are       when       and       when       what would we do if our calculated value of z were -2.80? when If     and       and the critical values of z are       when       and       when       what would we do if our calculated value of z were -2.80? and If     and       and the critical values of z are       when       and       when       what would we do if our calculated value of z were -2.80? when If     and       and the critical values of z are       when       and       when       what would we do if our calculated value of z were -2.80? what would we do if our calculated value of z were -2.80?

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We conduct a two-tailed test at the .05 significance level with data that afford 8 degrees of freedom. When we look up the critical value of t, we will expect it to be ____________ the corresponding critical value of z.

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When the value of When the value of     is changed from .05 to .01, is changed from .05 to .01,

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We are thinking of a two-tailed test, but decide on a one-tailed test. This means that

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As the number of degrees of freedom increases, student's distribution of t

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In general, "degrees of freedom" is most closely related to the

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When a one-tailed test is employed (rather than a two-tailed test),

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The answer to which of the following questions is the "key" to solving a statistical inference problem

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Glo-lite light bulbs are advertised as having an average life of 600 hours with a standard deviation of 20. Consumer's Advocates (CA) has received numerous complaints that the bulbs burn out much more quickly. In order to check on the validity of these complaints, CA tests a sample of 25 bulbs and obtains: Glo-lite light bulbs are advertised as having an average life of 600 hours with a standard deviation of 20. Consumer's Advocates (CA) has received numerous complaints that the bulbs burn out much more quickly. In order to check on the validity of these complaints, CA tests a sample of 25 bulbs and obtains:      (a)Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions.?(d)?Now repeat using    (a)Set up Glo-lite light bulbs are advertised as having an average life of 600 hours with a standard deviation of 20. Consumer's Advocates (CA) has received numerous complaints that the bulbs burn out much more quickly. In order to check on the validity of these complaints, CA tests a sample of 25 bulbs and obtains:      (a)Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions.?(d)?Now repeat using    and Glo-lite light bulbs are advertised as having an average life of 600 hours with a standard deviation of 20. Consumer's Advocates (CA) has received numerous complaints that the bulbs burn out much more quickly. In order to check on the validity of these complaints, CA tests a sample of 25 bulbs and obtains:      (a)Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions.?(d)?Now repeat using    (b)Perform the statistical test ( Glo-lite light bulbs are advertised as having an average life of 600 hours with a standard deviation of 20. Consumer's Advocates (CA) has received numerous complaints that the bulbs burn out much more quickly. In order to check on the validity of these complaints, CA tests a sample of 25 bulbs and obtains:      (a)Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions.?(d)?Now repeat using    (c)Draw final conclusions.?(d)?Now repeat using Glo-lite light bulbs are advertised as having an average life of 600 hours with a standard deviation of 20. Consumer's Advocates (CA) has received numerous complaints that the bulbs burn out much more quickly. In order to check on the validity of these complaints, CA tests a sample of 25 bulbs and obtains:      (a)Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions.?(d)?Now repeat using

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The mean of the t distribution

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We should probably use a lower value of We should probably use a lower value of    than usual when than usual when

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Ms. Phillips, research director of a large city school district, wishes to compare the mean score on a widely used reading readiness test of entering first graders in her district with the national norm of 62 and a standard deviation of 8. The results for a random sample of 10 children from her district are: Ms. Phillips, research director of a large city school district, wishes to compare the mean score on a widely used reading readiness test of entering first graders in her district with the national norm of 62 and a standard deviation of 8. The results for a random sample of 10 children from her district are:      (a) Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions. (d)Now repeat using    (a) Set up Ms. Phillips, research director of a large city school district, wishes to compare the mean score on a widely used reading readiness test of entering first graders in her district with the national norm of 62 and a standard deviation of 8. The results for a random sample of 10 children from her district are:      (a) Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions. (d)Now repeat using    and Ms. Phillips, research director of a large city school district, wishes to compare the mean score on a widely used reading readiness test of entering first graders in her district with the national norm of 62 and a standard deviation of 8. The results for a random sample of 10 children from her district are:      (a) Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions. (d)Now repeat using    (b)Perform the statistical test ( Ms. Phillips, research director of a large city school district, wishes to compare the mean score on a widely used reading readiness test of entering first graders in her district with the national norm of 62 and a standard deviation of 8. The results for a random sample of 10 children from her district are:      (a) Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions. (d)Now repeat using    (c)Draw final conclusions. (d)Now repeat using Ms. Phillips, research director of a large city school district, wishes to compare the mean score on a widely used reading readiness test of entering first graders in her district with the national norm of 62 and a standard deviation of 8. The results for a random sample of 10 children from her district are:      (a) Set up       and      (b)Perform the statistical test (     (c)Draw final conclusions. (d)Now repeat using

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If the outcome of a test is significant at the .05 level, it

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Statistic:parameter as

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The new Streamer four-cylinder compact is advertised as obtaining 39.2 miles per gallon (estimated highway mileage). A competitor doubts their claim and tests a sample of Streamers under highway conditions with the following results (in m.p.g.): 35, 41, 36, 32, 40, 38, 38, 36. Do these results cast doubt on the advertised claim?? (a)Set up The new Streamer four-cylinder compact is advertised as obtaining 39.2 miles per gallon (estimated highway mileage). A competitor doubts their claim and tests a sample of Streamers under highway conditions with the following results (in m.p.g.): 35, 41, 36, 32, 40, 38, 38, 36. Do these results cast doubt on the advertised claim??  (a)Set up       and       (b) Determine the critical value(s) of     (c)Perform the statistical test. (d)Draw final conclusions. and The new Streamer four-cylinder compact is advertised as obtaining 39.2 miles per gallon (estimated highway mileage). A competitor doubts their claim and tests a sample of Streamers under highway conditions with the following results (in m.p.g.): 35, 41, 36, 32, 40, 38, 38, 36. Do these results cast doubt on the advertised claim??  (a)Set up       and       (b) Determine the critical value(s) of     (c)Perform the statistical test. (d)Draw final conclusions. (b) Determine the critical value(s) of The new Streamer four-cylinder compact is advertised as obtaining 39.2 miles per gallon (estimated highway mileage). A competitor doubts their claim and tests a sample of Streamers under highway conditions with the following results (in m.p.g.): 35, 41, 36, 32, 40, 38, 38, 36. Do these results cast doubt on the advertised claim??  (a)Set up       and       (b) Determine the critical value(s) of     (c)Perform the statistical test. (d)Draw final conclusions. (c)Perform the statistical test. (d)Draw final conclusions.

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Which, if any, need not be decided in advance of conducting the test of a null hypothesis?

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A one-tailed test should be used when

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Compute the best estimates of Compute the best estimates of      and      for each of the following samples:? (a)pulse rate: 72, 86, 75, 66, 90;? (b)number of tumors per rat: 2, 7, 8, 6, 6, 11, 3. and Compute the best estimates of      and      for each of the following samples:? (a)pulse rate: 72, 86, 75, 66, 90;? (b)number of tumors per rat: 2, 7, 8, 6, 6, 11, 3. for each of the following samples:? (a)pulse rate: 72, 86, 75, 66, 90;? (b)number of tumors per rat: 2, 7, 8, 6, 6, 11, 3.

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