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O Mark 25 O Miu 25 OMAILSA b) What is the formula for your test statistic? O.& 。 米米 c) What value does your test statistic.T. take on with the sample data? [ bilik

O Mark 25 O Miu 25 OMAILSA b) What is the formula for your test statistic? O.& 。 米米 c) What value does your test statistic.T. take on with the sample data? [ bilik

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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The speeds of automobiles in the A23 construction zone are normally distributed with an unknown mean of u and an unknown standard deviation of o. The posted speed limit is 25 miles per hour (mph). Using a radar gun, a police officer took 10 independent measurements of the speeds of automobiles passing through the construction zoner. The measurements were (in mph):: 34, 27, 25, 29, 30, 30, 21, 32, 33, 27 We would like to test whether the mean mph in the A23 construction zone is greater than 25 mph. The null hypothesis is thus Ho:u=25. We will test this against the alternative Ha We want to test at the 5% level. Let x = the sample mean and s = the sample standard deviation. a) What should the alternative hypothesis, Ha, be? O H₂:4<25 OH₂:#25 O H₂:>25 O H₂:μ=25 O H₂:μ=5% b) What is the formula for your test statistic? OT = x 5% OT= OT= OT= OT= 4411 x-25 10 X-25 X-25 10 c) What value does your test statistic, T, take on with the sample data? d) What type of probability distribution does your test statistic, T, have? Ⓒnormal O Chi-Squared Ot O Cauchy O binomial
Transcribed Image Text:The speeds of automobiles in the A23 construction zone are normally distributed with an unknown mean of u and an unknown standard deviation of o. The posted speed limit is 25 miles per hour (mph). Using a radar gun, a police officer took 10 independent measurements of the speeds of automobiles passing through the construction zoner. The measurements were (in mph):: 34, 27, 25, 29, 30, 30, 21, 32, 33, 27 We would like to test whether the mean mph in the A23 construction zone is greater than 25 mph. The null hypothesis is thus Ho:u=25. We will test this against the alternative Ha We want to test at the 5% level. Let x = the sample mean and s = the sample standard deviation. a) What should the alternative hypothesis, Ha, be? O H₂:4<25 OH₂:#25 O H₂:>25 O H₂:μ=25 O H₂:μ=5% b) What is the formula for your test statistic? OT = x 5% OT= OT= OT= OT= 4411 x-25 10 X-25 X-25 10 c) What value does your test statistic, T, take on with the sample data? d) What type of probability distribution does your test statistic, T, have? Ⓒnormal O Chi-Squared Ot O Cauchy O binomial
c) What value does your test statistic, T, take on with the sample data? d) What type of probability distribution does your test statistic,T, have? normal O Chi-Squared Ot O Cauchy O binomial e) How many degrees of freedom does T have? f) Calculate the critical value, tstar, for your test.(negative value) g) For what values of your test statistic, T, is the null hypothesis rejected? OT> tstar or T < -tstar ⒸIT-tstar| < .05 OT> tstar/2 or T< -tstar/2 OT <tstar OT> tstar h) Calculate the p-value for this test. i) Is the null hypothesis rejected? (Y/N) ⒸY ON j) If we ran 1000 5% level tests then about how many times would we make a Type I error? k) k. Create a 95% confidence interval for the true average speed of automobiles in the A23 construction zone. ( 1) Copy your R script or any other comments for the above into the text box here.
Transcribed Image Text:c) What value does your test statistic, T, take on with the sample data? d) What type of probability distribution does your test statistic,T, have? normal O Chi-Squared Ot O Cauchy O binomial e) How many degrees of freedom does T have? f) Calculate the critical value, tstar, for your test.(negative value) g) For what values of your test statistic, T, is the null hypothesis rejected? OT> tstar or T < -tstar ⒸIT-tstar| < .05 OT> tstar/2 or T< -tstar/2 OT <tstar OT> tstar h) Calculate the p-value for this test. i) Is the null hypothesis rejected? (Y/N) ⒸY ON j) If we ran 1000 5% level tests then about how many times would we make a Type I error? k) k. Create a 95% confidence interval for the true average speed of automobiles in the A23 construction zone. ( 1) Copy your R script or any other comments for the above into the text box here.
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