Question

PURELL Advanced Instant Hand Sanitizer kills more than 99.99% of most common germs. This alcohol-based hand sanitizer works in as little as 15 seconds, with no water or towels needed. Bottles of PURELL are supposed to contain, on average, 2 fluid ounces. A random sample of bottles of PURELL was drawn, and the weight of each was recorded (in fluid ounces). The following data was obtained: 2.16, 1.98, 2.04, 2.01, 1.93, 1.99, 2.04, 2.05, 1.96, 2.01. It is assumed that the weight of bottles of PURELL is normally distributed in the population. Construct a 99% confidence interval estimate of the true population mean weight of all bottles of PURELL Advanced Instant Hand Sanitizer. Use only the appropriate formula and/or statistical table in your textbook to answer this question. Negative amounts should be indicated by a minus sign. Report your answer to 2 decimal places, using conventional rounding rules.

Answer 1

Solution:

x	x2
2.16	4.6656
1.98	3.9204
2.04	4.1616
2.01	4.0401
1.93	3.7249
1.99	3.9601
2.04	4.1616
2.05	4.2025
1.96	3.8416
2	4
∑x=20.16	∑x2=40.6784

Mean ˉx=∑xn

=2.16+1.98+2.04+2.01+1.93+1.99+2.04+2.05+1.96+2/10

=20.16/10

=2.016


Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√40.6784-(20.16)210/9

=√40.6784-40.6426/9

=√0.0358/9

=√0.004

=0.0631

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,9 =3.250

Margin of error = E = t/2,df * (s /n)

= 3.250 * (0.06 / 10)

= 0.06

Margin of error = 0.06

The 99% confidence interval estimate of the population mean is,

- E < < + E

2.02 - 0.06 < < 2.02 + 0.06

1.96 < < 2.08

(1.96 , 2.08 )