Hypothesis Testing About a Mean: Sigma Known

Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Hypothesis Testing
About a Mean: Sigma Known
Determine whether the given conditions justify testing a claim about a population mean μ.
1) The sample size is n = 25, σ = 5.93, and the original population is normally distributed.
2) The sample size is n = 17, σ is not known, and the original population is normally
distributed.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
1)
2)
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Identify the null hypothesis, alternative hypothesis, test statistic, P -value, conclusion about the null hypothesis, and
final conclusion that addresses the original claim.
3)
3) The health of employees is monitored by periodically weighing them in. A sample of 54
employees has a mean weight of 183.9 lb. Assuming that σ is known to be 121.2 lb, use a
0.10 significance level to test the claim that the population mean of all such employees
weights is less than 200 lb.
Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t
distribution, or neither.
4) Claim: μ = 959. Sample data: n = 25, x = 951, s = 25. The sample data appear to come from
a normally distributed population with σ = 28.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
4)
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic,
P-value, critical value(s), and state the final conclusion.
5)
5) Test the claim that for the adult population of one town, the mean annual salary is given
by μ = $30,000. Sample data are summarized as n = 17, x = $22,298, and s = $14,200. Use a
significance level of α = 0.05.
Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly
selected from a population with a normal distribution.
6)
6) Use a significance level of α = 0.01 to test the claim that μ > 2.85. The sample data consists
of 9 scores for which x = 3.25 and s = 0.53.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Answer Key
Testname: 29_HYPOTHESISTEST_MEAN_SIGMA
1) Yes
2) Yes
3) H0 : μ = 200; H1 : μ < 200; Test statistic: z = -0.98. P-value: 0.1635. Fail to reject H0 . There is not sufficient evidence to
warrrant the rejection of the claim that the mean equals 200.
4) Normal
5) α = 0.05
Test statistic: t = -2.24
P-value: p = 0.0399
Because t < -2.120, we reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that
μ = $30,000.
6) Test statistic: t = 2.26. Critical value: t = 2.896. Fail to reject H 0 : μ = 2.85. There is not sufficient evidence to support the
claim that the mean is greater than 2.85.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Hypothesis Testing
About a Mean: Sigma NOT Known
Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t
distribution, or neither.
1) Claim: μ = 119. Sample data: n = 15, x = 103, s = 15.2. The sample data appear to come from a
normally distributed population with unknown μ and σ.
A) Normal
B) Student t
C) Neither
1)
Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic,
P-value, critical value(s), and state the final conclusion.
2)
2) Test the claim that for the adult population of one town, the mean annual salary is given
by μ = $30,000. Sample data are summarized as n = 17, x = $22,298, and s = $14,200. Use a
significance level of α = 0.05.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
3) Test the claim that the mean age of the prison population in one city is less than 26 years .
3)
Sample data are summarized as n = 25, x = 24.4 years, and s = 9.2 years. Use a significance
level of α = 0.05.
Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly
selected from a population with a normal distribution.
4)
4) Use a significance level of α = 0.01 to test the claim that μ > 2.85. The sample data consists
of 9 scores for which x = 3.25 and s = 0.53.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
5) A public bus company official claims that the mean waiting time for bus number 14
during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours
on 18 different occasions. Her mean waiting time was 7 minutes with a standard deviation
of 2.3 minutes. At the 0.01 significance level, test the claim that the mean is less than 10
minutes.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
5)
Answer Key
Testname: 29(2)_HYPOTHESISTEST_MEAN_NOT SIGMA
1) B
2) α = 0.05
Test statistic: t = -2.24
P-value: p = 0.0399
Because t < -2.120, we reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that
μ = $30,000.
3) α = 0.05
Test statistic: t = -0.87
P-value: p = 0.1966
t > -1.711
Because t > -1.711, we do not reject the null hypothesis. There is not sufficient evidence to support the claim that the
mean age is less than 26 years.
4) Test statistic: t = 2.26. Critical value: t = 2.896. Fail to reject H 0 : μ = 2.85. There is not sufficient evidence to support the
claim that the mean is greater than 2.85.
5) Test statistic: t = -5.534. Critical values: t = -2.567. Reject H0 . There is sufficient evidence to support the claim that the
mean is less than 10 minutes.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley