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Pachacha [2.7K]
3 years ago
13

Suppose you are determining whether the depth of groves cut into aluminum by a milling machine is equal to 1.7 mm. You cut 14 gr

oves, then measure the depth of each one. With these measurements, you perform a statistical hypothesis test to determine whether the groove depth is equal to 1.7 mm. Which of the following tests would you use?
1. This one-sided test:
H0: μ = 1.7 mm
H1: μ < 1.7 mm
2. This one-sided test:
H0: μ = 1.7 mm
H1: μ > 1.7 mm
3. This two-sided test:
H0: μ = 1.7 mm
H1: μ ≠ 1.7 mm
4. This two-sided test:H0: μ > 1.7 mm
H1: μ = 1.5 mm
Mathematics
1 answer:
Gemiola [76]3 years ago
4 0

Answer:

For this case we want to check if the true mean for the depth of groves cut into aluminium by a machine is equal to 1.7 (null hypothesis) and the alternative hypothesis would be the complement different from 1.7. And the best system of hypothesis are:

Null hypothesis: \mu =1.7

Alternative hypothesis \mu \neq 1.7[/tx]And the best system of hypothesis are:3. This two-sided test:&#10;H0: μ = 1.7 mm&#10;H1: μ ≠ 1.7 mmStep-by-step explanation:For this case we want to check if the true mean for the depth of groves cut into aluminium by a machine is equal to 1.7 (null hypothesis) and the alternative hypothesis would be the complement different from 1.7. And the best system of hypothesis are:Null hypothesis: [tex]\mu =1.7

Alternative hypothesis [tex]\mu \neq 1.7[/tx]

And the best system of hypothesis are:

3. This two-sided test:

H0: μ = 1.7 mm

H1: μ ≠ 1.7 mm

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Answer:

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Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

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Where \mu=25 and \sigma=5

Part a

For this case we want to find this probability:

P(20 \leq X \leq 30) = P(20-0.5 \leq X \leq 30+0.5)

And if we use the z score given by:

z =\frac{x-\mu}{\sigma}

We got this:

P(19.5 \leq X \leq 30.5) = P(\frac{19.5-25}{5} \leq Z \leq \frac{30.5 -25}{5})=P(-1.1 \leq Z \leq 1.1)

And we can find this probability like this:

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Part b

For this case we want this probability:

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And if we use the continuity correction we got:

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And using the z score we got:

P(X

Part c

For this case we want this probability:

P(X

And if we use the continuity correction we got:

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