Births by Day of Week 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:

(a) Write the null and alternative hypotheses.

(b) State the requirements that must be satisfied to use the oneway ANOVA procedure.

(c) Use the following Minitab output to test the hypothesis of equal means at the  level of significance.

(d) Shown are side-by-side boxplots for each weekday. Do these boxplots support the results obtained in part (c)?

Diversity and pH The following data represent the number of fish species living in various Andirondack Lakes and the pH of the lakes. From chemistry, we know pH is a measure of the acidity or basicity of a solution. Solutions with pH less than 7 are said to be acidic. As pH increases, the solution is said to be less acidic.

(a) Draw a scatter diagram of the data treating pH as the explanatory variable.

(b) Determine the linear correlation coefficient between pH and number of fish species.

(c) Does a linear relation exist between pH and number of fish species?

(d) Find the least-squares regression line treating pH as the explanatory variable.

(e) Interpret the slope.

(f) Is it reasonable to interpret the intercept? Explain.

(g) What proportion of the variability in number of fish species is explained by pH?

(h) Is the number of fish species in the lake whose pH is 5.5 above or below average? Explain.

(i) In part (g), you found the proportion of variability in number of fish species that is explained by the variability in pH. Can you think of other variables that might also explain the variability in the number of fish species?