Question

The table contains the data from an urban school district on the number of eighth‑grade students with three or more unexcused absences from school during each month of a school year. Because the total number of eighth‑graders changes a bit from month to month, these totals are also given for each month.

	Sept.	Oct.	Nov.	Dec.	Jan.	Feb.	Mar.	Apr.	May	June
Students	811	847	839	842	818	820	831	825	802	783
Absent	251	309	324	295	261	282	304	284	263	304

(a) Calculate p¯. Round your answer to 5 decimal places.

p¯=

Because the number of students varies from month to month, also find n¯, the average number of students per month. (Enter your answer rounded to one decimal place.)

?⎯=

(b) Make a ? chart using control limits based on n¯ students each month. Find the upper and lower bounds on the control limits. (Enter your answers rounded to five decimal places.)

???=

???=

What do the data suggest about control?

1)The data suggest that absentee rates are not in control.

2)The data suggest that absentee rates are in control.

(c) The exact control limits are different each month because the number of students n is different each month. This situation is common in using p charts. What are the exact limits for October, the month with the largest n ? (Enter your answers rounded to four decimal places.)

October ???=

October ???=

What are the exact limits for June, the month with the smallest n? (Enter your answers rounded to five decimal places.)

June ???=

June ???=

Add these limits to your p chart, using short lines spanning a single month. How do these limits affect your conclusions?

1)We cannot draw any conclusions from this data.

2)Smaller samples yield wider limits, but the difference here is negligible. The sample sizes would need to vary much more in order to effect a large change in limits from month‑to‑month.

3)Larger samples yield wider limits, but the difference here is negligible. The sample sizes would need to vary much more in order to effect a large change in limits from month‑to‑month.

Answer 1