Two-Tailed Hypothesis Tests and CIs. As we mentioned on page 386, the following relationship holds between hypothe- sis tests and confidence intervals for one-mean z-procedures: For a two-tailed hypothesis test at the significance level α, the null hypothesis H0: μ = μ0 will be rejected in favor of the alternative hypothesis Ha: μ = μ0 if and only if μ0 lies outside the (1 − α)- level confidence interval for μ. In each case, illustrate the preced- ing relationship by obtaining the appropriate one-mean z-interval (Procedure 8.1 on page 330) and comparing the result to the con- clusion of the hypothesis test in the specified exercise. a. Exercise 9.74 b. Exercise 9.77 Exercise 9.74: 9.74 Agriculture Books. The R. R. Bowker Company col- lects information on the retail prices of books and publishes the data in The Bowker Annual Library and Book Trade Almanac. In 2005, the mean retail price of agriculture books was $57.61. 9.4 Hypothesis Tests for One Population Mean When σ Is Known 389 This year’s retail prices for 28 randomly selected agriculture books are shown in the following table. 59.54 67.70 57.10 46.11 46.86 62.87 66.40 52.08 37.67 50.47 60.42 38.14 58.21 47.35 50.45 71.03 48.14 66.18 59.36 41.63 53.66 49.95 59.08 58.04 46.65 66.76 50.61 66.68 At the 10% significance level, do the data provide sufficient evi- dence to conclude that this year’s mean retail price of agriculture books has changed from the 2005 mean? Assume that the popula- tion standard deviation of prices for this year’s agriculture books is $8.45. (Note: The sum of the data is $1539.14.)
Two-Tailed Hypothesis Tests and CIs. As we mentioned
on page 386, the following relationship holds between hypothe-
sis tests and confidence intervals for one-mean z-procedures: For
a two-tailed hypothesis test at the significance level α, the null
hypothesis H0: μ = μ0 will be rejected in favor of the alternative
hypothesis Ha: μ = μ0 if and only if μ0 lies outside the (1 − α)-
level confidence interval for μ. In each case, illustrate the preced-
ing relationship by obtaining the appropriate one-mean z-interval
(Procedure 8.1 on page 330) and comparing the result to the con-
clusion of the hypothesis test in the specified exercise.
a. Exercise 9.74 b. Exercise 9.77
Exercise 9.74:
9.74 Agriculture Books. The R. R. Bowker Company col-
lects information on the retail prices of books and publishes the
data in The Bowker Annual Library and Book Trade Almanac.
In 2005, the mean retail price of agriculture books was $57.61.
9.4 Hypothesis Tests for One Population Mean When σ Is Known 389
This year’s retail prices for 28 randomly selected agriculture
books are shown in the following table.
59.54 67.70 57.10 46.11 46.86 62.87 66.40
52.08 37.67 50.47 60.42 38.14 58.21 47.35
50.45 71.03 48.14 66.18 59.36 41.63 53.66
49.95 59.08 58.04 46.65 66.76 50.61 66.68
At the 10% significance level, do the data provide sufficient evi-
dence to conclude that this year’s mean retail price of agriculture
books has changed from the 2005 mean? Assume that the popula-
tion standard deviation of prices for this year’s agriculture books
is $8.45. (Note: The sum of the data is $1539.14.)
Exercise 9.77:
Serving Time. According to the Bureau of Crime Statis-
tics and Research of Australia, as reported on Lawlink, the mean
length of imprisonment for motor-vehicle-theft offenders in Aus-
tralia is 16.7 months. One hundred randomly selected motor-
vehicle-theft offenders in Sydney, Australia, had a mean length
of imprisonment of 17.8 months. At the 5% significance level,
do the data provide sufficient evidence to conclude that the mean
length of imprisonment for motor-vehicle-theft offenders in Syd-
ney differs from the national mean in Australia? Assume that the
population standard deviation of the lengths of imprisonment for
motor-vehicle-theft offenders in Sydney is 6.0 months.
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