The complete question is stated below:
An obstetrician knew that there were more live births during the week than on weekends. She wanted to determine whether the mean number of births was the same for each of the five days of the week. She randomly selected eight dates for each of the five days of the week and obtained the following data:
Monday: Tuesday: Wednesday: Thursday: Friday:
10,456 11,621 11,084 11,171 11,545
10,023 11,944 11,570 11,745 12,321
10,691 11,045 11,346 12,023 11,749
10,283 12,927 11,875 12,433 12,192
10,265 12,577 12,193 12,132 12,422
11,189 11,753 11,593 11,903 11,627
11,198 12,509 11,216 11,233 11,624
11,465 13,521 11,818 12,543 12,543
a. Write the null and alternative hypotheses.
b. State the requirements that must be satisfied to use the one-way ANOVA procedure.
c On which day or dates are there more births?
a. Null Hypothesis: There is no statistically significant difference between the mean number of babies born alive on Mondays, Tuesdays, Wednesdays, Thursdays and Fridays.
Alternative Hypothesis: The mean number of babies born alive on each weekday from Monday to Friday are not the same.
b) 1. The dependent variable should be measured at ratio or interval level
2. The independent variable should contain at least two groups that are categorical and independent
3. There must independence of observations between and within the various groups
4. No significant outliers should exist
5. for each group of the independent variable, the dependent variable should be approximately normally distributed.
6. the variances should be homogeneous
c. There are more births on Tuesdays and Fridays
Step-by-step explanation:
a. A Null Hypothesis is one that states that no statistical significance exist between the two variables in the hypothesis. It is the null hypothesis that the researcher tries to disprove. While the alternative hypothesis is simply the opposite of the null hypothesis, it hypothesizes that there is indeed a statistically significant relationship between the variables in question.
b. 1. The dependent variable should be measured at ratio or interval level; among the various levels of measurements such as ordinal, nominal, ratio or interval, the dependent variable must be either on the interval or ratio level.
2. The independent variable should contain at least two groups that are categorical and independent; the independent variable, in this case, the number of live births, should be two groups or more, and they should be categorical.
3. There must independence of observations between and within the various groups; the values observed within each group should be independent of the other. For example, no one pregnant woman should be involved in more than one group.
4. No significant outliers should exist; outliers are single data points within the measured variable that do not follow the usual point pattern of the other values, either values that are too high or too low. they reduce the accuracy of the one-way ANOVA.
5. for each group of the independent variable, the dependent variable should be approximately normally distributed; violations of normality causes the result to be invalid. It can only hold little variations to produce valid results.
6. the variances should be homogeneous; the variances (distribution or spread around the mean) of the two or more test groups must be considered equal.
c. Tuesday with a mean livebirth of 12,237 births and Friday with an average livebirth of 12,002 births have the most number of births.
