A electronics manufacturer has developed a new type of remote control button that is designed to operate longer before failing to work consistently. A random sample of 23 of the new buttons is selected and each is tested in continuous operation until it fails to work consistently. The resulting lifetimes are found to have a sample mean of x¯ = 1274.2 hours and a sample standard deviation of s = 114. Independent tests reveal that the mean lifetime of the best remote control button on the market is 1210 hours. Conduct a hypothesis test to determine if the new button's mean lifetime exceeds 1210 hours. Round all calculated answers to four decimal places.

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wifilethbridge wifilethbridge · Answer 1 · 2019-11-22T07:36:34+01:00

Answer:

Claim : if the new button's mean lifetime exceeds 1210 hours.

[tex]H_0:\mu = 1210\\H_a:\mu > 1210[/tex]

Sample mean = [tex]\bar{x}=1274.2[/tex]

Sample standard deviation s = 114

n = 23

Since n < 30 and sample standard deviation is given .

So, we will use t test

Formula : [tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}}[/tex]

Substitute the values :

[tex]t=\frac{1274.2-1210}{\frac{114}{\sqrt{23}}}[/tex]

[tex]t=2.7008[/tex]

degree of freedom = n-1 = 23-1 =22

confidence level = 95%

Significance level = 5%

[tex]t_{df,\frac{\alpha}{2}}=t_{22,\frac{0.05}{2}}=1.7170[/tex]

t calculated > t critical

So, we failed to accept null hypothesis

Thus the new button's mean lifetime exceeds 1210 hours.