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Unformatted text preview: 1331 are not shown. Glow TwoTailed Tests About a Population Mean:
σ Known
s Excel Value Worksheet
A
1 Weight
2
6.04
3
5.99
4
5.92
5
6.03
6
6.01
7
5.95
8
6.09
9
6.07
10
6.07
11
5.97
12
5.96 B
Sample Size 30
Sample Mean 6.1
Population Std. Dev. 0.2
Hypothesized Value 6
Standard Error 0.0365
Test Statistic z 2.7386
p Value (lower tail) 0.9969
p Value (upper tail) 0.0031
p Value (two tail) 0.0062 Note: Rows 1331 are not shown. C Glow TwoTailed Tests About a Population Mean:
σ Known Critical Value Approach
4. Determine the critical value and rejection rule.
For α /2 = .03/2 = .015, z.015 = 2.17
Reject H0 if z < 2.17 or z > 2.17
5. Determine whether to reject H0.
Because 2.74 > 2.17, we reject H0.
There is sufficient statistical evidence to
infer that the alternative hypothesis is true (i.e. the mean filling weight is not 6 ounces). Glow TwoTailed Tests About a Population Mean:
σ Known Glow Critical Value Approach Sampling
distribution
x − µ0
z of =
σ/ n
Reject H0 Reject H0 Do Not Reject H0 α/2 = .015 2.17 α/2 = .015
0 2.17 z Confidence Interval Approach to
TwoTailed Tests About a Population
Mean Select a simple random sample from the population
x and use the value of the sample mean to develop the confidence interval for the population mean µ . (Confidence intervals are covered in Chapter 8.) If the confidence interval contains the hypothesized value µ 0, do not reject H0. Otherwise, reject H0. Confidence Interval Approach to
TwoTailed Tests About a Population
Mean
Glow The 97% confidence interval for µ is
σ
x ± zα / 2
= 6.1 ± 2.17(.2 30) = 6.1 ± .07924
n
or 6.02076 to 6.17924 Because the hypothesized value for the
population mean, µ 0 = 6, is not in this interval,
the hypothesistesting conclusion is that the
null hypothesis, H0: µ = 6, can be rejected. Tests About a Population
Mean:
σ Unknown • Test Statistic x − µ0
t=
s/ n This test statistic has a t distribution with n 1 degrees of freedom. Tests About a Population
Mean:
σ Unknown
s Rejection Rule: p Value Approach
Reject H0 if p –value < α
s Rejection Rule: Critical Value Approach
H0: µ > µ 0 Reject H0 if t < tα H0: µ < µ 0 Reject H0 if t > tα H0: µ = µ 0 Reject H0 if t < tα/2 or t > tα/2 p Values and the t Distribution The format of the t distribution table provided in most statistics textbooks does not have sufficient detail to determine the exact pvalue for a hypothesis test. However, we can still use the t distribution table to identify a range for the pvalue. An advantage of computer software packages is that the computer output will provide the pvalue for the t distribution. Example: Highway Patrol
• OneTailed Test About a Population Mean: σ Unknown A State Highway Patrol periodically samples vehicle speeds at various locations
on a particular roadway. The sample of vehicle speeds
is used to test the hypothesis
H0: µ < 65 The locations where H0 is rejected are deemed
the best locations for radar traps. Example: Highway Patrol
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This note was uploaded on 08/28/2011 for the course BUS 300 taught by Professor White during the Spring '09 term at Rutgers.
 Spring '09
 White

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