1. ACCORDING TO THE COMMISSION OF HIGHER EDUCATION, FACULTY MEMBERS WORK AN AVERAGE OF 30 HOURS PER WEEK DURING THE SCHOOL YEAR . A REGIONAL DIRECTOR

OF A CERTAIN SCHOOL SURVEYED 35 RANDOMLY SELECTED FACULTY MEMBERS AND FOUND THAT THEY WORK AN AVERAGE OF 35 HOURS A WEEK AND THE STANDARD DEVIATION

WAS 2.75 HOURS , TEST IF THE MEAN NUMBER OF HOURS WORKED BY THE FACULTY MEMBERS IN THE REGIONAL DIRECTOR'S SCHOOL DIFFERS FROM THE NATIONAL AVERAGE .

USE ALPHA = .01

2. AN AGRONOMIST BELIEVES THAT A NEWLY DEVELOPED FERTILIZER WILL INCREASE THE MEAN HARVEST OF SQUASH BY 50 KGS. FIFTY - SIX PLANTS WERE TREATED WITH FERTILIZER

AND HAD A MEAN HARVEST OF 95 KGS. WITH STANDARD DEVIATION OF 2.7 KGS. FORTY - NINE PLANTS WERE UNTREATED AND HAD A MEAN HARVEST OF 9.25 KGS. WITH STANDARD

DEVIATION OF 0.7 KG. TEST THE CLAIM AT ALPHA = 0.05 LEVEL OF SIGNIFICANCE.

3. THE DAILY SALES OF TWO NEWSPAPER VENDORS WERE RECORDED ON A RANDOM BASIS . THE RESULTS OF THE TWO SAMPLES ARE AS FOLLOWS :

VENDOR A VENDOR B

P 1080 P 1130

P 1250 P 1200

P 1300 P 1200

P 1160 P 1100

P 1200 P 1250

P 1190 P 1200

IS THERE A SIGNIFICANT DIFFERENCE BETWEEN THE MEAN SALES OF THE TWO NEWSPAPER VENDORS ? TEST AT ALPHA = 0.01 SIGNIFICANCE LEVEL .

4. A REGISTRAR OF A CERTAIN UNIVERSITY CLAIMS THAT 55% OF THE ACCOUNTING STUDENTS CHANGE THEIR MAJOR SUBJECT TO ANOTHER AREA AFTER THEIR SECOND YEAR IN THE

PROGRAM DUE TO RETENTION POLICY . A RANDOM SAMPLE OF 125 STUDENTS IN THE COLLEGE OF ACCOUNTANCY REVEALED THAT 50 STUDENTS HAD CHANGED THEIR MAJOR

SUBJECT TO ECONOMICS , MARKETING , BANKING AND FINANCE , MANAGEMENT AFTER THEIR SECOND YEAR . IS THERE A DECREASE IN THE PROPORTION OF STUDENTS WHO CHANGED THEIR

MAJOR AFTER THEIR SECOND YEAR IN THE PROGRAM ? TEST AT THE .05 LEVEL OF SIGNIFICANCE .

5. A TOOTHPASTE COMPANY CLAIMS THAT THE TRUE MEAN WEIGHT OF TOOTH PASTE IN EACH BOXES LABELED " 150g " . TO TEST THIS HYPOTHESIS , A MARKETING RESEARCHER RANDOMLY

SAMPLES 200 BOXES OF THE COMPANY'S TOOTHPASTE , FINDING A SAMPLE MEAN OF 148.9 g WITH A SAMPLE STANDARD DEVIATION OF 21.3 g. TEST THE COMPANY'S CLAIM AT .05

LEVEL OF SIGNIFICANCE.