LAB 3: TESTS ABOUT A POPULATION MEAN
Confidence interval:
Exercise:
The data set lowbt (on website) contains information recorded for a sample of 100 low birth weight infants born in two teaching hospitals in Boston, Massachusetts. Measurements of systolic blood pressure are saved under the variable name sbp, while indicators of gender- where 1 represents a male and 0 female- are saved under the name sex.
a) Compute a 95% confidence interval for the true mean systolic blood pressure of male low birth weight infants.
(Hint: Use Select Cases so that only the males are selected.)
Data →Select cases
Analyze →Compare Means →One sample t test
95% confidence interval for the true mean systolic blood pressure of male low birth weight infants is: (……………)
b) Calculate a 95% confidence interval for the true mean systolic blood pressure of female low birth weight infants.
95% confidence interval for the true mean systolic blood pressure of female low birth weight infants is: (………………..)
c) Calculate a 90% confidence interval for true mean systolic blood pressure of female and male low birth weight infants.
Data →Split File
Testing one mean
One-sample t-test:
The One SampletTest determines whether the sample mean is statistically different from a known or hypothesized population mean. The One SampletTest is a parametric test.
This test is also known as:
· Single SampletTest
The variable used in this test is known as:
· Test variable
Note:The Test Variable is compared against a Test Value, which is the known or hypothesized mean in the population.
Exercise:
The Bayley Scales of Infant Development yield scores on two indices-the Psychomotor Development Index (PDI) and the Mental Development Index (MDI)- which can be used to assess a child’s level of functioning in each of these areas at approximately one year of age. Among normal healthy infants, both indices have a mean value of 100. As part of a study assessing the development and neurologic status of children who have undergone reparative heart surgery during the three months of life, the Bayley Scales were administered to a sample of one year old infants born with congenital heart disease. The data contained in the data set heart; PDI scores are saved under the variable pdi, while MDI scores are saved under mdi.
a) At the 0.05 level of significance, test the null hypothesis that the mean PDI score for children born with congenital heart disease who undergo reparative heart surgery during the first three months of life is equal to 100, the mean score for healthy children. Use a two sided test. What is the p-value? What do you conclude?
Analyze → Compare Means →One-Sample T Test
The researcher can use the degrees of freedom value to locate the critical t value associated with his or her chosen alpha and then follow the procedure of comparing t-calculated to t-table.
The p value, labeled as “Sig (2-tailed)” in the results table can be used to test the hypothesis. If the p-value lies under the standard alpha value of .05 then using this alpha value one would reject the null hypothesis.
b) Conduct the analogous test of hypothesis for the mean MDI score. What do you conclude?
c) Construct a 95% confidence intervals for the true mean PDI score and the true mean MDI score for this population of children with congenital heart disease. Does either of these intervals contain the value of 100? Would you have expected that they would?
Wilcoxon signed rank test:
Exercise:
Use minidat data on the webpage to test whether the median of height variable is equal to 75.
1. First check for normality using Kolmogorov Smirnov test.
Analyze →Nonparametric test →One sample →Fields
Settings →Customize tests →Test observed distribution…(Kolmogrov-Smirnov) → Options →Normal
Is the data normally distributed?
2. If the data is not normally distributed apply Wilcoxon signed rank t
Analyze →Nonparametric test →One sample →Settings →Compare Median
What do you conclude?
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