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 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.