Question

The operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. He took a random sample of his remote controls and tested two

asked Aug 20, 2021 51.7k views

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Jehonathan Thomas · Answer 1 · 2021-08-26T15:28:12+0000

Answer:

$t=\frac{107.75-116.75}{\sqrt{(2.75^2)/(4)+(9.604^2)/(4)}}}=-1.802$

The degrees of freedom are given by:

df=n_(1)+n_(2)-2=4+4-2=6

The p value for this case would be given by:

p_v =2*P(t_((6))<-1.804)=0.121

Since the p value is higher than the significance level we have enough evidence to FAIl to reject the null hypothesis and we can conclude that the true mean is not significantly different between the two types of battery

Explanation:

Information given

Battery 1 106 111 109 105

Battery 2 125 103 121 118

We can calculate the mean and the deviation with the following formulas"

$\bar X =(\sum_(i=1)^n X_i)/(n)$

$s =\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}$

$\bar X_(1)=107.75$ represent the mean for the Battery 1

$\bar X_(2)=116.75$ represent the mean for the Bettery 2

s_(1)=2.75 represent the sample standard deviation for the Battery 1

s_(2)=9.604 represent the sample standard deviation for the battery 2

n_(1)=4 sample size selected for the Battery 1

n_(2)=4 sample size selected for the Battery 2

$\alpha=0.1$ represent the significance level

t would represent the statistic

p_v represent the p value

System of hypothesis

We want to check if the difference in longevity between the two batteries, the system of hypothesis would be:

Null hypothesis:
$\mu_(1) = \mu_(2)$

Alternative hypothesis:
$\mu_(1) \\eq \mu_(2)$

The statistic is given by:

$t=\frac{\bar X_(s1)-\bar X_(2)}{\sqrt{(s^2_(1))/(n_(1))+(s^2_(2))/(n_(2))}}$ (1)