Answered

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A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of bolts. The sample mean bolt length was centimeters. The population standard deviation is known to be centimeters.
What is the test statistic z?What is the p-value?Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of α=0.1?

Sagot :

Cricetus

Answer:

There is sufficient evidence. A further explanation is provided below.

Step-by-step explanation:

According to the question,

The alternative as well as null hypothesis will be:

[tex]H_0:\mu = 16[/tex]

[tex]H_a:\mu>16[/tex]

The test statistics will be:

⇒ [tex]z = \frac{\frac{\bar x - \mu}{\sigma} }{\sqrt{n} }[/tex]

By putting the values, we get

⇒    [tex]=\frac{\frac{16.06-16}{0.24} }{\sqrt{96} }[/tex]

⇒    [tex]=\frac{\frac{0.06}{0.24} }{\sqrt{96} }[/tex]

⇒    [tex]=2.45[/tex]

Or,

The p-value will be:

= 0.0071

i.e.,

⇒ [tex]p-value< \alpha[/tex]

Thus the above is the correct answer.

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