A. Several studies have shown that women with many children are less likely to get ovarian cancer. In a new study, data are collected from 25 women ages 40−49 with ovarian cancer. The mean parity (number of children) of these women is 1.8 with standard deviation 1.2. Suppose the mean number of children among women in the general population in this age group is 2.5. What test can be used to test the hypothesis that women with ovarian cancer have fewer children than women in the general population in the same age group? Perform the test in A1 using the critical-value method. What is the p-value based on the test in A1? What do you conclude from this study?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Answer A1, A2, and B1:
A. Several studies have shown that women with many children are less likely to get ovarian cancer. In a new study, data are collected from 25 women ages 40−49 with ovarian cancer. The mean parity (number of children) of these women is 1.8 with standard deviation 1.2. Suppose the mean number of children among women in the general population in this age group is 2.5.
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- What test can be used to test the hypothesis that women with ovarian cancer have fewer children than women in the general population in the same age group?
- Perform the test in A1 using the critical-value method.
- What is the p-value based on the test in A1?
- What do you conclude from this study?
B. The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL.
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- If the mean and standard deviation of serum creatinine in the general population are 1.0 and 0.4 mg/dL, respectively, then, using significance level of .05, test whether the mean serum-creatinine level in this group is different from that of the general population.
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