### Hypothesis Testing for Mean Nickel DiameterThe 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.#### ObjectiveTest 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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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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Mean, Median, Mode

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Question

### 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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