The accuracy of a coin-counter machine is gauged to accept nickels with a mean diameter of millimeters 21.21 mm. A sample of 47 nickles was drawn from a reported defective coin-counter machine located near a school. The sample had a sample mean of 21.212 mm and sample standard deviation 0.01 mm. Test the claim that the mean nickel diameter accepted by this coin-counter machine is greater than 21.21 mm. Test at the 0.01 significance level. (a) Identify the correct alternative hypothesis Ha: Ομ= 21.21 Ομ< 21.21 Ομ> 21.21 Give all answers correct to 4 decimal places. (b) The test statistic value is: (c) Using the Traditional method, the critical value is: (d) Based on your answers above, do you: O Reject Ho O Fail to reject Ho (e) Explain your choice in the box below. (f) Based on your work above, choose one of the following conclusions of your test: O There is not sufficient evidence to support the claim O The sample data supports the claim O There is not sufficient evidence to warrant rejection of the claim O There is sufficient evidence to warrant rejection of the claim (g) Explain your choice in the box below.
The accuracy of a coin-counter machine is gauged to accept nickels with a mean diameter of millimeters 21.21 mm. A sample of 47 nickles was drawn from a reported defective coin-counter machine located near a school. The sample had a sample mean of 21.212 mm and sample standard deviation 0.01 mm. Test the claim that the mean nickel diameter accepted by this coin-counter machine is greater than 21.21 mm. Test at the 0.01 significance level. (a) Identify the correct alternative hypothesis Ha: Ομ= 21.21 Ομ< 21.21 Ομ> 21.21 Give all answers correct to 4 decimal places. (b) The test statistic value is: (c) Using the Traditional method, the critical value is: (d) Based on your answers above, do you: O Reject Ho O Fail to reject Ho (e) Explain your choice in the box below. (f) Based on your work above, choose one of the following conclusions of your test: O There is not sufficient evidence to support the claim O The sample data supports the claim O There is not sufficient evidence to warrant rejection of the claim O There is sufficient evidence to warrant rejection of the claim (g) Explain your choice in the box below.
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![### Hypothesis Testing for Mean Nickel Diameter
The accuracy of a coin-counter machine is gauged to accept nickels with a mean diameter of 21.21 mm. A sample of 47 nickels was drawn from a reported defective coin-counter machine located near a school. The sample had a sample mean of 21.212 mm and sample standard deviation 0.01 mm.
#### Objective
Test the claim that the mean nickel diameter accepted by this coin-counter machine is greater than 21.21 mm. Test at the 0.01 significance level.
#### Steps for Hypothesis Testing
(a) **Identify the correct alternative hypothesis \( H_a \):**
\[
\begin{aligned}
&\mid \mu = 21.21 \\
&\mid \mu < 21.21 \\
&\mid \mu > 21.21 \\
\end{aligned}
\]
(b) **Calculate the test statistic value:**
\[
\text{The test statistic value is: } \boxed{\hspace{100pt}}
\]
(c) **Determine the critical value using the Traditional method:**
\[
\text{Using the Traditional method, the critical value is: } \boxed{\hspace{100pt}}
\]
(d) **Based on your answers above, make a decision:**
\[
\begin{aligned}
&\mid \text{Reject } H_0 \\
&\mid \text{Fail to reject } H_0 \\
\end{aligned}
\]
(e) **Explain your choice:**
\[
\boxed{\hspace{350pt}}
\]
(f) **Based on your work above, choose one of the following conclusions of your test:**
\[
\begin{aligned}
&\mid \text{There is not sufficient evidence to support the claim} \\
&\mid \text{The sample data supports the claim} \\
&\mid \text{There is not sufficient evidence to warrant rejection of the claim} \\
&\mid \text{There is sufficient evidence to warrant rejection of the claim} \\
\end{aligned}
\]
(g) **Explain your choice:**
\[
\boxed{\hspace{350pt}}
\]
Please ensure all answers are precise, accurate, and correct to 4 decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F010d10ea-7975-4510-a7a7-5e4f696daa17%2F1c8c2b7d-5896-44d3-8a93-2302e9326785%2Filkzkmc_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Mean Nickel Diameter
The accuracy of a coin-counter machine is gauged to accept nickels with a mean diameter of 21.21 mm. A sample of 47 nickels was drawn from a reported defective coin-counter machine located near a school. The sample had a sample mean of 21.212 mm and sample standard deviation 0.01 mm.
#### Objective
Test the claim that the mean nickel diameter accepted by this coin-counter machine is greater than 21.21 mm. Test at the 0.01 significance level.
#### Steps for Hypothesis Testing
(a) **Identify the correct alternative hypothesis \( H_a \):**
\[
\begin{aligned}
&\mid \mu = 21.21 \\
&\mid \mu < 21.21 \\
&\mid \mu > 21.21 \\
\end{aligned}
\]
(b) **Calculate the test statistic value:**
\[
\text{The test statistic value is: } \boxed{\hspace{100pt}}
\]
(c) **Determine the critical value using the Traditional method:**
\[
\text{Using the Traditional method, the critical value is: } \boxed{\hspace{100pt}}
\]
(d) **Based on your answers above, make a decision:**
\[
\begin{aligned}
&\mid \text{Reject } H_0 \\
&\mid \text{Fail to reject } H_0 \\
\end{aligned}
\]
(e) **Explain your choice:**
\[
\boxed{\hspace{350pt}}
\]
(f) **Based on your work above, choose one of the following conclusions of your test:**
\[
\begin{aligned}
&\mid \text{There is not sufficient evidence to support the claim} \\
&\mid \text{The sample data supports the claim} \\
&\mid \text{There is not sufficient evidence to warrant rejection of the claim} \\
&\mid \text{There is sufficient evidence to warrant rejection of the claim} \\
\end{aligned}
\]
(g) **Explain your choice:**
\[
\boxed{\hspace{350pt}}
\]
Please ensure all answers are precise, accurate, and correct to 4 decimal places.
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