作业帮Hypothesis Testing
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Hypothesis Testing
In a study of iron deficiency among infants, the blood hemoglobin levels were compared between two samples of infants, who follow different feeding regimes. One group consisted of breast fed infants, while the other group was fed with a standard baby formula without any iron supplements. The summary of results on blood hemoglobin levels for infants at 12 months of age is as follows:
Group Sample size Mean Standard deviation
Breast –fed 23 13.3 1.7
Baby formula 19 12.4 1.8
Is there sufficient evidence to indicate that the mean blood hemoglobin level is higher among the breast-fed babies? Test at = 0.05.
[sp2 = 3.0475; t = 1.663; Do not reject H0]
In a study of iron deficiency among infants, the blood hemoglobin levels were compared between two samples of infants, who follow different feeding regimes. One group consisted of breast fed infants, while the other group was fed with a standard baby formula without any iron supplements. The summary of results on blood hemoglobin levels for infants at 12 months of age is as follows:
Group Sample size Mean Standard deviation
Breast –fed 23 13.3 1.7
Baby formula 19 12.4 1.8
Is there sufficient evidence to indicate that the mean blood hemoglobin level is higher among the breast-fed babies? Test at = 0.05.
[sp2 = 3.0475; t = 1.663; Do not reject H0]
Hypothesis:A statement about the value of a population parameter developed for the purpose of testing.
Hypothesis testing:假设检验 Based on sample evidence and probability theory; Used to determine whether the hypothesis is a reasonable statement and should not be rejected,or is unreasonable and should be rejected.
Step One:State the null and alternate hypotheses
Null Hypothesis H0 零假设或空假设:A statement about the value of a population parameter
Alternative Hypothesis H1备择假设:A statement that is accepted if the sample data provide evidence that the null hypothesis is false
Three possibilities regarding means(The null hypothesis always contains equality.)
H0:μ=0 H0:μ≤0 H0:μ≥0
H1:μ≠0 H1:μ>0 H1:μ Critical z
p-Value:The probability,assuming that the null hypothesis is true,of finding a value of the test statistic at least as extreme as the computed value for the test
Decision Rule:If the p-Value is larger than or equal to the significance level,a,H0 is not rejected.If the p-Value is smaller than the significance level,a,H0 is rejected.
Calculated from the probability distribution function or by computer
P-value< level of significance:reject H0
P-value > level of significance:fail to reject H0
Step Five:Make a decision.
One-Tailed Tests of Significance:The alternate hypothesis,H1,states a direction
Two-Tailed Tests of Significance:No direction is specified in the alternate hypothesis H1.
Test for the population mean from a large sample with population standard deviation known
Proportion:The sample proportion is p and p is the population proportion.
The fraction or percentage that indicates the part of the population or sample having a particular trait of interest.
Test Statistic for Testing a Single Population Proportion
Hypothesis testing:假设检验 Based on sample evidence and probability theory; Used to determine whether the hypothesis is a reasonable statement and should not be rejected,or is unreasonable and should be rejected.
Step One:State the null and alternate hypotheses
Null Hypothesis H0 零假设或空假设:A statement about the value of a population parameter
Alternative Hypothesis H1备择假设:A statement that is accepted if the sample data provide evidence that the null hypothesis is false
Three possibilities regarding means(The null hypothesis always contains equality.)
H0:μ=0 H0:μ≤0 H0:μ≥0
H1:μ≠0 H1:μ>0 H1:μ Critical z
p-Value:The probability,assuming that the null hypothesis is true,of finding a value of the test statistic at least as extreme as the computed value for the test
Decision Rule:If the p-Value is larger than or equal to the significance level,a,H0 is not rejected.If the p-Value is smaller than the significance level,a,H0 is rejected.
Calculated from the probability distribution function or by computer
P-value< level of significance:reject H0
P-value > level of significance:fail to reject H0
Step Five:Make a decision.
One-Tailed Tests of Significance:The alternate hypothesis,H1,states a direction
Two-Tailed Tests of Significance:No direction is specified in the alternate hypothesis H1.
Test for the population mean from a large sample with population standard deviation known
Proportion:The sample proportion is p and p is the population proportion.
The fraction or percentage that indicates the part of the population or sample having a particular trait of interest.
Test Statistic for Testing a Single Population Proportion