Question

how to solve by hand?

12. A packaging company conducts a survey for the two new package designs for lunch boxes in a supermarket. The results are as follows: Dasion 158.5 Design2 150.3 138.4 168.1 149.4 145.8 168. 7 154.4 162.9 135.4 131.6 158.8 131.4 150.8 161.4 137.6 156.8 147.6 a. What is the range of the true (or population) mean of the data in each design for 80% confidence level? b. Calculate the standard normal distribution z and P(z) for each data set.

Answer 1

a)

Design 1	Design 2
158.5	150.3
138.4	155.4
168.1	151.6
149.4	158.8
145.8	151.4
168.7	150.8
154.4	161.4
162.9	157.6
	156.8
	147.6
155.775	154.17	mean
10.83035	4.443235	sd
8	10	n
1.414924	1.383029	t
5.417894	1.943258	t* s/sqrt(n)
150.3571	152.2267	lower
161.1929	156.1133	upper

for Design 1

(150.3571,161.1929)

For Design 2

(185.2267,156.1133

Formula in Excel

Design 1	Design 2
158.5	150.3
138.4	155.4
168.1	151.6
149.4	158.8
145.8	151.4
168.7	150.8
154.4	161.4
162.9	157.6
	156.8
	147.6
=AVERAGE(A2:A11)	=AVERAGE(B2:B11)	mean
=STDEV(A2:A11)	=STDEV(B2:B11)	sd
=COUNT(A2:A11)	=COUNT(B2:B11)	n
=T.INV(0.9,A15-1)	=T.INV(0.9,B15-1)	t
=A17*A14/SQRT(A15)	=B17*B14/SQRT(B15)	t* s/sqrt(n)
=A13-A18	=B13-B18	lowe
=A13+A18	=B13+B18	upper

b)

z for Design 1	z for Design 2
0.2516	-0.8710
-1.6043	0.2768
1.1380	-0.5784
-0.5886	1.0420
-0.9210	-0.6234
1.1934	-0.7585
-0.1270	1.6272
0.6579	0.7720
	0.5919
	-1.4787

Design 1	Design 2		z for Design 1	z for Design 2
158.5	150.3		=(A2-155.775)/10.83035	=(B2-154.17)/4.443235
138.4	155.4		=(A3-155.775)/10.83035	=(B3-154.17)/4.443235
168.1	151.6		=(A4-155.775)/10.83035	=(B4-154.17)/4.443235
149.4	158.8		=(A5-155.775)/10.83035	=(B5-154.17)/4.443235
145.8	151.4		=(A6-155.775)/10.83035	=(B6-154.17)/4.443235
168.7	150.8		=(A7-155.775)/10.83035	=(B7-154.17)/4.443235
154.4	161.4		=(A8-155.775)/10.83035	=(B8-154.17)/4.443235
162.9	157.6		=(A9-155.775)/10.83035	=(B9-154.17)/4.443235
	156.8			=(B10-154.17)/4.443235
	147.6			=(B11-154.17)/4.443235