Question 1115160: A government-sponsored telephone counseling service for adolescents tested
whether the length of calls would be affected by a special telephone system that
had a better sound quality. Over the past several years, the lengths of telephone
calls (in minutes) were normally distributed with = 18 and = 8. They
arranged to have the special phone system loaned to them for one day. On that
day, the mean length of the 46 calls they received was 21 minutes. Test whether
the length of calls has changed using the 5% significance level. (a) Carry
out a Z test using the five steps of hypothesis testing. (b) Make a drawing of
the distributions involved. (c) Explain your answer to someone who knows
about hypothesis testing with a sample of a single individual but who knows
nothing about hypothesis testing with samples of more than one individual.
(d) ADVANCED TOPIC: Figure the 95% confidence interval.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A government-sponsored telephone counseling service for adolescents tested
whether the length of calls would be affected by a special telephone system that
had a better sound quality. Over the past several years, the lengths of telephone
calls (in minutes) were normally distributed with mu = 18 and sigma = 8. They
arranged to have the special phone system loaned to them for one day.
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On that day, the mean length of the 46 calls they received was 21 minutes. Test whether the length of calls has changed using the 5% significance level.
(a) Carry out a Z test using the five steps of hypothesis testing.
Ho: u1-u2 = 0
Ha: u1-u2 # 0
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sample difference:: 18-21 = -3
reject intervals:: z< -1.96 and z > 1.96
test statistic:: z(-3) = (-3)/sqrt[(8^2/n1^2)+(s2^2/n2)]
Note:: n1, n2, and s2 are missing from your post.
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(b) Make a drawing of
the distributions involved. (c) Explain your answer to someone who knows
about hypothesis testing with a sample of a single individual but who knows
nothing about hypothesis testing with samples of more than one individual.
(d) ADVANCED TOPIC: Figure the 95% confidence interval.
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