1. Hypothesis testing examples
from Weiers

2. a = .05 Page 380, Problem 10.44 Hypothesis: m = 8.7 years.
Local YMCA: Average membership age is 8.7 years.
Hypothesis: m = 8.7 years.
Sample: n = 15 member files.
X = 7.2 years
S = 2.5 years
a = .05

3. t( ) = Page 380, Problem 10.44 Hypothesis: m = 1.76 cups per day.
Local YMCA: Average membership age is 8.7 years.
Hypothesis: m = 1.76 cups per day.
n = 15
Form a 95% confidence interval:
X = 7.2 years
t( ) =
2.145
.025, 14
S = 2.5 years
a = .05
2.5 15
7.2 ± 
7.2 ±
My 95% CI is (5.8154, ) years.

4. The true mean age of membership a the local YMCA is not 8.7 years.
Page 380, Problem 10.44
Local YMCA: Average membership age is 8.7 years.
Hypothesis: m = 8.7 years.
My 95% CI is (5.8154, )
Decision:
Since 8.7 does NOT fall within my CI, reject the hypothesis. 8.7 is NOT a plausible value for the true mean.
Conclusion:
The true mean age of membership a the local YMCA is not 8.7 years.

5. a = .05 Page 380, Problem 10.42 Hypothesis: m = 1.76 cups per day.
International Coffee Association reports for the population of US residents over 10 years of age
mean daily coffee consumption is 1.76 cups per day.
Hypothesis: m = 1.76 cups per day.
Sample: n = 38 people over 10 years from a North Carolina city.
X = 1.96 cups per day
S = .85 cups per day
a = .05

6. t( ) = Page 380, Problem 10.42 Hypothesis: m = 1.76 cups per day.
Is the true population mean for this city different than that for all US residents over 10 years of age?
Hypothesis: m = 1.76 cups per day.
n = 38
Form a 95% confidence interval:
X = 1.96 cups/day
t( ) =
2.026
.025, 37
S = .85 cups/day
a = .05
.85 38
1.96 ± 2.026
1.96 ± .2794
My 95% CI is (1.6806, ) cups per day.

7. Hypothesis: m = 1.76 cups per day.
Page 380, Problem 10.42
Is the true population mean for this city different than that for all US residents over 10 years of age?
Hypothesis: m = 1.76 cups per day.
My 95% CI is (1.6806, )
Decision:
Since 1.76 DOES fall within my CI, do not reject the hypothesis.
Conclusion:
There is not sufficient evidence to indicate that the mean coffee consumption for residents of this North Carolina city over the age of 10 is different than that of all US residents over the age of 10.