Confidence interval for the proportion of employees

Question

Assignment:

Q: The employee benefits manager of a small private university would like to estimate the proportion of full-time employees who prefer adopting the first (i.e., plan A) of three available health care plans in the coming annual enrollment period. A reliable frame of the university's employees and their tentative preferences are in the file P08_25.xlsx.

a. Use Excel to choose a simple random sample of size 45 from the given frame.

b. Use the sample found in part a. to construct a 99% confidence interval for the proportion of university employees who prefer plan A. Assume that the population consists of the preferences of all employees in the given frame.

c. Interpret the 99% confidence interval constructed in Part b.

Continuing Problem, select simple random samples of 30 individuals from each of the given employee classifications (i.e., administrative staff, support staff, and faculty). Construct a 99% confidence interval for the proportion of employees who prefer adopting plan A for each of the classifications. Do you see evidence of significant differences among these three interval estimates. Summarize your findings.

Health Care Plan Preferences for a Given Private University's Employees

Employee	Classification	Selection
1	3	Plan B
2	1	Plan C
3	2	Plan B
4	3	Plan B
5	2	Plan B
6	2	Plan A
7	2	Plan C
8	2	Plan C
9	2	Plan B
10	2	Plan B
11	3	Plan B
12	2	Plan A
13	2	Plan A
14	1	Plan B
15	2	Plan C
16	3	Plan C
17	2	Plan A
18	2	Plan C
19	1	Plan B
20	2	Plan C
21	1	Plan B
22	1	Plan B
23	3	Plan A
24	2	Plan B
25	2	Plan B
26	3	Plan C
27	1	Plan B
28	3	Plan A
29	2	Plan A
30	3	Plan A
31	2	Plan B
32	2	Plan A
33	1	Plan C
34	2	Plan B
35	2	Plan B
36	2	Plan C
37	2	Plan B
38	1	Plan A
39	2	Plan A
40	2	Plan A
41	1	Plan B
42	3	Plan C
43	1	Plan C
44	2	Plan A
45	1	Plan A
46	2	Plan C
47	3	Plan A
48	2	Plan A
49	3	Plan A
50	2	Plan C
51	2	Plan C
52	3	Plan B
53	2	Plan A
54	2	Plan C
55	1	Plan A
56	2	Plan A
57	2	Plan C
58	1	Plan C
59	3	Plan B
60	2	Plan A
61	3	Plan A
62	3	Plan C
63	1	Plan B
64	2	Plan A
65	2	Plan C
66	2	Plan C
67	3	Plan A
68	3	Plan A
69	3	Plan A
70	2	Plan A
71	2	Plan A
72	3	Plan B
73	3	Plan B
74	2	Plan A
75	1	Plan A
76	2	Plan C
77	2	Plan C
78	3	Plan B
79	2	Plan C
80	2	Plan C
81	1	Plan C
82	3	Plan A
83	1	Plan B
84	2	Plan A
85	1	Plan A
86	2	Plan C
87	1	Plan B
88	1	Plan B
89	2	Plan B
90	1	Plan C
91	3	Plan A
92	2	Plan B
93	2	Plan C
94	2	Plan B
95	1	Plan A
96	3	Plan A
97	2	Plan C
98	1	Plan B
99	1	Plan B
100	2	Plan A
101	2	Plan A
102	2	Plan C
103	3	Plan C
104	2	Plan B
105	2	Plan C
106	1	Plan B
107	2	Plan B
108	2	Plan A
109	2	Plan A
110	2	Plan A
111	2	Plan B
112	2	Plan A
113	2	Plan B
114	2	Plan C
115	2	Plan A
116	3	Plan A
117	2	Plan A
118	1	Plan A
119	3	Plan C
120	2	Plan B
121	2	Plan B
122	2	Plan C
123	3	Plan B
124	1	Plan A
125	2	Plan B
126	2	Plan B
127	2	Plan A
128	1	Plan B
129	3	Plan C
130	3	Plan C
131	3	Plan C
132	2	Plan C
133	2	Plan B
134	3	Plan C
135	2	Plan B
136	3	Plan A
137	1	Plan B
138	1	Plan A
139	1	Plan A
140	1	Plan A
141	3	Plan B
142	2	Plan A
143	3	Plan B
144	1	Plan B
145	2	Plan A
146	1	Plan B
147	2	Plan C
148	2	Plan B
149	2	Plan C
150	3	Plan A
151	1	Plan C
152	3	Plan A
153	2	Plan B
154	1	Plan B
155	2	Plan B
156	3	Plan A
157	2	Plan B
158	1	Plan A
159	1	Plan B
160	2	Plan B
161	2	Plan B
162	3	Plan C
163	3	Plan C
164	2	Plan B
165	2	Plan C
166	1	Plan B
167	1	Plan C
168	3	Plan B
169	3	Plan C
170	3	Plan A
171	2	Plan B
172	2	Plan B
173	1	Plan B
174	2	Plan B
175	3	Plan A
176	2	Plan B
177	1	Plan B
178	1	Plan A
179	2	Plan A
180	1	Plan B
181	2	Plan C
182	1	Plan A
183	3	Plan C
184	2	Plan C
185	2	Plan B
186	3	Plan B
187	2	Plan C
188	2	Plan C
189	2	Plan B
190	1	Plan B
191	1	Plan B
192	1	Plan B
193	1	Plan B
194	3	Plan B
195	2	Plan B
196	2	Plan C
197	2	Plan A
198	2	Plan B
199	2	Plan C
200	2	Plan C
201	3	Plan B
202	1	Plan B
203	3	Plan C
204	2	Plan B
205	2	Plan B
206	1	Plan B
207	1	Plan A
208	1	Plan B
209	3	Plan C
210	3	Plan B
211	3	Plan B
212	3	Plan C
213	3	Plan A
214	3	Plan B
215	2	Plan B
216	1	Plan B
217	1	Plan A
218	2	Plan B
219	2	Plan C
220	3	Plan A
221	3	Plan A
222	1	Plan B
223	2	Plan B
224	1	Plan B
225	2	Plan C
226	2	Plan C
227	2	Plan A
228	3	Plan C
229	1	Plan A
230	2	Plan A
231	2	Plan A
232	1	Plan C
233	2	Plan C
234	3	Plan C
235	1	Plan B
236	2	Plan B
237	2	Plan C
238	2	Plan C
239	2	Plan B
240	3	Plan B
241	2	Plan A
242	2	Plan C
243	2	Plan C
244	2	Plan A
245	1	Plan A
246	1	Plan A
247	2	Plan C
248	2	Plan B
249	2	Plan B
250	2	Plan C
251	2	Plan C
252	2	Plan C
253	1	Plan C
254	1	Plan A
255	2	Plan C
256	3	Plan B
257	3	Plan C
258	3	Plan C
259	3	Plan A
260	3	Plan C
261	1	Plan A
262	1	Plan C
263	3	Plan A
264	2	Plan B
265	1	Plan C
266	2	Plan C
267	3	Plan B
268	2	Plan B
269	2	Plan A
270	2	Plan C
271	2	Plan B
272	1	Plan A
273	1	Plan B
274	2	Plan B
275	3	Plan A
276	2	Plan C
277	2	Plan C
278	2	Plan B
279	1	Plan A
280	2	Plan B
281	2	Plan A
282	3	Plan B
283	1	Plan B
284	2	Plan C
285	3	Plan B
286	2	Plan C
287	1	Plan B
288	2	Plan C
289	2	Plan B
290	3	Plan B
291	3	Plan C
292	2	Plan B
293	2	Plan B
294	1	Plan A
295	3	Plan B
296	2	Plan C
297	3	Plan B
298	2	Plan B
299	2	Plan B
300	3	Plan B
301	2	Plan A
302	2	Plan C
303	2	Plan C
304	1	Plan A
305	3	Plan C
306	1	Plan B
307	1	Plan A
308	2	Plan C
309	3	Plan A
310	2	Plan A
311	2	Plan B
312	1	Plan A
313	1	Plan C
314	2	Plan B
315	3	Plan A
316	2	Plan C
317	2	Plan B
318	3	Plan A
319	1	Plan B
320	2	Plan B
321	2	Plan B
322	2	Plan B
323	2	Plan A
324	2	Plan C
325	1	Plan C
326	3	Plan A
327	3	Plan C
328	1	Plan A
329	2	Plan B
330	1	Plan B
331	2	Plan A
332	2	Plan B
333	2	Plan B
334	1	Plan A
335	2	Plan B
336	1	Plan A
337	1	Plan C
338	2	Plan C
339	1	Plan C
340	3	Plan B
341	3	Plan A
342	2	Plan A
343	2	Plan C
344	2	Plan C
345	3	Plan A
346	3	Plan C
347	1	Plan C
348	2	Plan C
349	3	Plan C
350	3	Plan A
351	3	Plan B
352	2	Plan B
353	2	Plan C
354	3	Plan A
355	1	Plan A
356	2	Plan A
357	1	Plan B
358	2	Plan A
359	1	Plan B
360	3	Plan B
361	1	Plan A
362	2	Plan B
363	2	Plan A
364	2	Plan C
365	2	Plan B
366	3	Plan B
367	2	Plan C
368	1	Plan B
369	2	Plan B
370	2	Plan A
371	2	Plan B
372	2	Plan C
373	2	Plan C
374	2	Plan C
375	3	Plan A
376	3	Plan B
377	2	Plan B
378	3	Plan A
379	1	Plan A
380	3	Plan C
381	2	Plan C
382	3	Plan B
383	2	Plan B
384	2	Plan C
385	3	Plan A
386	3	Plan C
387	3	Plan C
388	1	Plan A
389	1	Plan A
390	2	Plan A
391	1	Plan A
392	2	Plan A
393	2	Plan A
394	2	Plan A
395	2	Plan B
396	3	Plan B
397	3	Plan A
398	2	Plan C
399	2	Plan B
400	2	Plan C
401	3	Plan A
402	3	Plan C
403	3	Plan A
404	3	Plan A
405	1	Plan A
406	2	Plan B
407	1	Plan C
408	3	Plan A
409	2	Plan A
410	3	Plan B
411	1	Plan B
412	3	Plan B
413	2	Plan C
414	2	Plan B
415	1	Plan B
416	3	Plan A
417	3	Plan C
418	2	Plan C
419	2	Plan B
420	1	Plan B
421	3	Plan A
422	3	Plan B
423	2	Plan A
424	2	Plan A
425	1	Plan B
426	2	Plan A
427	2	Plan C
428	3	Plan A
429	3	Plan C
430	1	Plan A
431	1	Plan B
432	1	Plan B
433	2	Plan C
434	2	Plan C
435	3	Plan C
436	2	Plan C
437	2	Plan C
438	1	Plan B
439	2	Plan B
440	3	Plan A
441	3	Plan A
442	1	Plan A
443	2	Plan A
444	1	Plan A
445	1	Plan A
446	1	Plan A
447	3	Plan A
448	2	Plan C
449	1	Plan B
450	2	Plan C
451	2	Plan C
452	3	Plan B
453	2	Plan B
454	1	Plan B
455	2	Plan B
456	2	Plan A
457	3	Plan C
458	2	Plan C
459	2	Plan C
460	3	Plan B
461	3	Plan C
462	2	Plan A
463	2	Plan C
464	3	Plan A
465	3	Plan A
466	1	Plan B
467	3	Plan C
468	2	Plan A
469	3	Plan B
470	3	Plan B
471	2	Plan C
472	2	Plan A
473	2	Plan B
474	2	Plan B
475	1	Plan B
476	3	Plan A
477	3	Plan B
478	1	Plan C
479	2	Plan B
480	2	Plan B
481	3	Plan B
482	3	Plan C
483	2	Plan B
484	2	Plan B
485	1	Plan C
486	3	Plan C
487	3	Plan B
488	2	Plan A
489	3	Plan A
490	3	Plan B
491	2	Plan A
492	2	Plan C
493	2	Plan C
494	2	Plan B
495	3	Plan A
496	1	Plan B
497	2	Plan A
498	1	Plan A
499	1	Plan A
500	1	Plan C
501	2	Plan A
502	3	Plan A
503	2	Plan A
504	1	Plan B
505	3	Plan B
506	3	Plan A
507	2	Plan C
508	2	Plan B
509	3	Plan B
510	2	Plan B
511	2	Plan C
512	3	Plan C
513	3	Plan A
514	2	Plan B
515	2	Plan B
516	3	Plan B
517	2	Plan A
518	3	Plan B
519	2	Plan A
520	3	Plan B
521	2	Plan A
522	2	Plan C
523	3	Plan B
524	1	Plan B
525	1	Plan A
526	3	Plan B
527	3	Plan B
528	1	Plan B
529	2	Plan A
530	2	Plan A
531	2	Plan A
532	3	Plan B
533	2	Plan C
534	2	Plan B
535	2	Plan C
536	2	Plan A
537	1	Plan B
538	2	Plan A
539	2	Plan A
540	3	Plan B
541	1	Plan A
542	1	Plan C
543	2	Plan C
544	1	Plan A
545	2	Plan C
546	2	Plan A
547	2	Plan A
548	2	Plan A
549	1	Plan A
550	2	Plan C
551	1	Plan B
552	3	Plan A
553	1	Plan A
554	2	Plan B
555	2	Plan A
556	2	Plan C
557	2	Plan B
558	2	Plan B
559	1	Plan A
560	2	Plan A
561	1	Plan A
562	1	Plan A
563	2	Plan C
564	2	Plan A
565	2	Plan B
566	2	Plan A
567	3	Plan B
568	2	Plan A
569	1	Plan A
570	3	Plan A
571	2	Plan C
572	1	Plan B
573	1	Plan C
574	2	Plan A
575	2	Plan C
576	1	Plan A
577	2	Plan B
578	3	Plan A
579	3	Plan B
580	2	Plan A
581	3	Plan B
582	3	Plan B
583	3	Plan A
584	2	Plan B
585	3	Plan C
586	1	Plan A
587	1	Plan A
588	3	Plan A
589	1	Plan A
590	2	Plan A
591	3	Plan B
592	2	Plan C
593	2	Plan A
594	1	Plan A
595	3	Plan A
596	2	Plan A
597	3	Plan B
598	1	Plan B
599	3	Plan A
600	3	Plan A
601	2	Plan B
602	2	Plan A
603	1	Plan A
604	3	Plan A
605	1	Plan A
606	1	Plan C
607	2	Plan B
608	3	Plan B
609	2	Plan A
610	1	Plan B
611	3	Plan B
612	2	Plan B
613	2	Plan A
614	1	Plan B
615	2	Plan B
616	2	Plan A
617	1	Plan A
618	3	Plan A
619	1	Plan B
620	3	Plan A
621	3	Plan C
622	2	Plan C
623	2	Plan B
624	2	Plan B
625	3	Plan B
626	2	Plan C
627	3	Plan A
628	2	Plan B
629	2	Plan B
630	3	Plan B
631	1	Plan C
632	3	Plan B
633	3	Plan B
634	2	Plan B
635	1	Plan B
636	3	Plan A
637	2	Plan C
638	2	Plan B
639	3	Plan B
640	1	Plan B
641	3	Plan C
642	2	Plan B
643	3	Plan A
644	2	Plan B
645	1	Plan A
646	1	Plan A
647	3	Plan C
648	2	Plan C
649	2	Plan B
650	2	Plan C
651	2	Plan B
652	2	Plan A
653	3	Plan C
654	1	Plan C
655	1	Plan B
656	2	Plan C
657	3	Plan B
658	2	Plan B
659	3	Plan C
660	2	Plan B
661	1	Plan B
662	3	Plan C
663	3	Plan B
664	2	Plan B
665	1	Plan A
666	1	Plan A
667	2	Plan B
668	3	Plan B
669	2	Plan C
670	2	Plan C
671	3	Plan B
672	1	Plan C
673	1	Plan A
674	2	Plan C
675	1	Plan C
676	3	Plan C
677	2	Plan A
678	3	Plan C
679	2	Plan A
680	2	Plan B
681	1	Plan B
682	1	Plan B
683	2	Plan B
684	2	Plan A
685	2	Plan A
686	3	Plan B
687	2	Plan A
688	2	Plan C
689	2	Plan B
690	2	Plan B
691	1	Plan B
692	1	Plan A
693	2	Plan C
694	2	Plan C
695	2	Plan C
696	2	Plan B
697	2	Plan C
698	3	Plan A
699	3	Plan B
700	3	Plan B
701	3	Plan A
702	2	Plan B
703	2	Plan C
704	2	Plan B
705	2	Plan A
706	2	Plan B
707	1	Plan A
708	2	Plan A
709	3	Plan A
710	2	Plan B
711	1	Plan B
712	1	Plan B
713	1	Plan A
714	3	Plan B
715	3	Plan A
716	2	Plan B
717	2	Plan B
718	2	Plan C
719	1	Plan B
720	2	Plan A
721	2	Plan C
722	2	Plan B
723	2	Plan B
724	2	Plan A
725	1	Plan C
726	3	Plan C
727	3	Plan A
728	2	Plan A
729	2	Plan C
730	1	Plan A
731	2	Plan C
732	2	Plan A
733	2	Plan A
734	3	Plan A
735	3	Plan B
736	2	Plan B
737	3	Plan B
738	2	Plan C
739	3	Plan A
740	3	Plan B
741	2	Plan B
742	2	Plan A
743	2	Plan B
744	2	Plan C
745	2	Plan A
746	3	Plan A
747	2	Plan C
748	1	Plan B
749	2	Plan B
750	2	Plan C
751	1	Plan B
752	2	Plan C
753	1	Plan B
754	1	Plan B
755	1	Plan A
756	2	Plan B
757	1	Plan C
758	3	Plan A
759	2	Plan C
760	3	Plan A
761	1	Plan A
762	2	Plan C
763	2	Plan B
764	3	Plan B
765	2	Plan C
766	2	Plan A
767	2	Plan A
768	2	Plan B
769	2	Plan A
770	3	Plan C
771	3	Plan A
772	2	Plan C
773	2	Plan B
774	2	Plan A
775	3	Plan B
776	3	Plan A
777	2	Plan B
778	3	Plan A
779	2	Plan B
780	3	Plan A
781	2	Plan B
782	2	Plan B
783	2	Plan B
784	1	Plan C
785	3	Plan A
786	2	Plan B
787	3	Plan B
788	1	Plan C
789	2	Plan B
790	2	Plan C
791	2	Plan C
792	3	Plan A
793	3	Plan B
794	2	Plan C
795	1	Plan C
796	1	Plan B
797	2	Plan B
798	2	Plan C
799	2	Plan A
800	1	Plan B
801	2	Plan C
802	1	Plan B
803	3	Plan B
804	2	Plan A
805	2	Plan A
806	2	Plan C
807	3	Plan B
808	1	Plan C
809	2	Plan C
810	1	Plan B
811	2	Plan C
812	3	Plan B
813	2	Plan A
814	2	Plan B
815	2	Plan C
816	1	Plan A
817	1	Plan A
818	1	Plan B
819	2	Plan C
820	3	Plan B
821	3	Plan B
822	3	Plan B
823	2	Plan B
824	2	Plan C
825	1	Plan B
826	1	Plan B
827	2	Plan B
828	3	Plan B
829	1	Plan B
830	3	Plan B
831	2	Plan A
832	1	Plan A
833	1	Plan B
834	2	Plan A
835	3	Plan A
836	1	Plan B
837	2	Plan A
838	3	Plan B
839	3	Plan B
840	1	Plan A
841	2	Plan B
842	3	Plan C
843	3	Plan C
844	2	Plan B
845	1	Plan A
846	3	Plan C
847	1	Plan A
848	3	Plan A
849	2	Plan A
850	3	Plan B
851	2	Plan B
852	1	Plan A
853	2	Plan C
854	2	Plan A
855	3	Plan C
856	1	Plan C
857	2	Plan C
858	1	Plan A
859	1	Plan C
860	3	Plan A
861	2	Plan A
862	1	Plan C
863	2	Plan B
864	2	Plan A
865	1	Plan B
866	2	Plan A
867	1	Plan A
868	2	Plan A
869	2	Plan C
870	2	Plan C
871	3	Plan B
872	2	Plan B
873	2	Plan B
874	1	Plan B
875	1	Plan B
876	3	Plan A
877	2	Plan B
878	3	Plan B
879	2	Plan C
880	2	Plan B
881	2	Plan A
882	2	Plan A
883	2	Plan B
884	2	Plan B
885	1	Plan C
886	1	Plan A
887	3	Plan C
888	2	Plan B
889	2	Plan A
890	2	Plan C
891	1	Plan B
892	1	Plan A
893	2	Plan B
894	2	Plan A
895	1	Plan A
896	3	Plan A
897	1	Plan A
898	3	Plan A
899	2	Plan B
900	1	Plan A
901	1	Plan B
902	2	Plan C
903	1	Plan B
904	1	Plan C
905	2	Plan A
906	1	Plan A
907	2	Plan A
908	3	Plan A
909	3	Plan B
910	1	Plan C
911	3	Plan A
912	2	Plan C
913	2	Plan B
914	2	Plan C
915	1	Plan A
916	2	Plan B
917	3	Plan A
918	1	Plan A
919	1	Plan A
920	3	Plan B
921	2	Plan B
922	1	Plan B
923	2	Plan C
924	1	Plan B
925	3	Plan A
926	2	Plan C
927	3	Plan B
928	2	Plan B
929	3	Plan A
930	1	Plan C
931	2	Plan B
932	3	Plan B
933	3	Plan A
934	2	Plan A
935	2	Plan B
936	1	Plan C
937	2	Plan C
938	1	Plan A
939	1	Plan B
940	1	Plan B