Question

MEDICO Corporation makes several portable electronic devices used in hospitals. Some of these products require rechargeable batteries that MEDICO purchases from various suppliers. Although they try to find them at the best price, they must also consider the quality. In one case, two suppliers were being considered. A test was run on the time the batteries would last in a certain device before it had to be recharged. The results are given in the table below.

a) What are the two populations being studied in this problem?

b) Define the population parameters u1 & u2 .

Supplier	Batteries used in test	Sample Mean Life	Sample Standard Deviation
Power+	32	25 Hours	5.2
Electro	40	23 Hours	2.7

c)  Set up the null and alternative hypotheses and run the test to see if the sample data supports the conclusion that the rechargeable batteries sold by Power+ last longer. Use a=.05

d) ) State your conclusion in the context of the problem.

Answer 1

A) The two populations are the batteries uesd in power+ and the batteries used in Electro.

B) = The population mean number of batteries used in Power+

= The population mean number of batteries used in Electro.

C) H₀:  

H₁:

The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

= (25 - 23)/sqrt((5.2)^2/32 + (2.7)^2/40)

= 1.97

Df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

= ((5.2)^2/32 + (2.7)^2/40)^2/(((5.2)^2/32)^2/31 + ((2.7)^2/40)^2/39) = 44

At alpha = 0.05, the critical value is t^* = 1.680

D) Since the test statistic value is greater than the critical value (1.97 > 1.680), so we should reject the null hypothesis.

So there is sufficient evidence to support the claim that the rechargeable batteries sold by power+ last longer.