Questions: on each run are shown in the accompanying data table. Complete parts a through c. a. The potential buyer wants to know whether the sample data refute the manufacturer's claim. Specify the null and alt Choose the correct answer below. A. H0: μ=10 H0: μ=10 Ha: μ>10 c. H0: μ=10 Ha: μ ≠ 10 b. In the context of this exercise, what is a Type I error? A Type II error? First identify what a Type I error is for this situation. Choose the correct answer below. Data table 10 8 9 9 12 9 11 8 8 10 6 9 6 11 10 10 10 13 8 11 11 9 12 7 8 9 9 6 12 5 9 9 10 9 7 8 11 11 10 1 9 12 11 10 6 9 10 10 A. A Type I error would be to conclude that the true mean number of solder joints inspected is not equal to 10 wh B. A Type I error would be to conclude that the sample mean number of solder joints inspected is greater than 10 C. A Type I error would be to conclude that the true mean number of solder joints inspected is less than 10 when, D. A Type I error would be to conclude that the true mean number of solder joints inspected is equal to 10 when, Now identify what a Type II error is for this situation. Choose the correct answer below. A. A Type II error would be to conclude that the true mean number of solder joints inspected is 10 when, in fact, the mean is less than 10. B. A Type II error would be to conclude that the true mean number of solder joints inspected is less than 10 when, in fact, the mean is equal to 10. C. A Type II error would be to conclude that the true mean number of solder joints inspected is not equal to 10 when, in fact, the mean is equal to 10. D. A Type II error would be to conclude that the sample mean number of solder joints inspected is 10 when, in fact, the mean is greater than 10. c. Conduct the hypothesis test you described in part a and interpret the test's results in the context of this exercise. Use α=0.05. Calculate the value of the test statistic. z= (Round to two decimal places as needed.)

on each run are shown in the accompanying data table. Complete parts a through c. a. The potential buyer wants to know whether the sample data refute the manufacturer's claim. Specify the null and alt Choose the correct answer below. A. H0: μ=10 H0: μ=10 Ha: μ>10 c. H0: μ=10 Ha: μ ≠ 10 b. In the context of this exercise, what is a Type I error? A Type II error? First identify what a Type I error is for this situation. Choose the correct answer below. Data table 10 8 9 9 12 9 11 8 8 10 6 9 6 11 10 10 10 13 8 11 11 9 12 7 8 9 9 6 12 5 9 9 10 9 7 8 11 11 10 1 9 12 11 10 6 9 10 10 A. A Type I error would be to conclude that the true mean number of solder joints inspected is not equal to 10 wh B. A Type I error would be to conclude that the sample mean number of solder joints inspected is greater than 10 C. A Type I error would be to conclude that the true mean number of solder joints inspected is less than 10 when, D. A Type I error would be to conclude that the true mean number of solder joints inspected is equal to 10 when, Now identify what a Type II error is for this situation. Choose the correct answer below. A. A Type II error would be to conclude that the true mean number of solder joints inspected is 10 when, in fact, the mean is less than 10. B. A Type II error would be to conclude that the true mean number of solder joints inspected is less than 10 when, in fact, the mean is equal to 10. C. A Type II error would be to conclude that the true mean number of solder joints inspected is not equal to 10 when, in fact, the mean is equal to 10. D. A Type II error would be to conclude that the sample mean number of solder joints inspected is 10 when, in fact, the mean is greater than 10. c. Conduct the hypothesis test you described in part a and interpret the test's results in the context of this exercise. Use α=0.05. Calculate the value of the test statistic. z= (Round to two decimal places as needed.)
Transcript text: on each run are shown in the accompanying data table. Complete parts a through c. a. The potential buyer wants to know whether the sample data refute the manufacturer's claim. Specify the null and alt Choose the correct answer below. A. $H_{0}: \mu=10$ \[ \begin{array}{l} H_{0}: \mu=10 \\ H_{a}: \mu>10 \end{array} \] c. \[ \begin{array}{l} H_{0}: \mu=10 \\ H_{a}: \mu \neq 10 \end{array} \] b. In the context of this exercise, what is a Type I error? A Type II error? First identify what a Type I error is for this situation. Choose the correct answer below. Data table \begin{tabular}{|ccccccccccccc|} \hline 10 & 8 & 9 & 9 & 12 & 9 & 11 & 8 & 8 & 10 & 6 & 9 & \\ 6 & 11 & 10 & 10 & 10 & 13 & 8 & 11 & 11 & 9 & 12 & 7 \\ 8 & 9 & 9 & 6 & 12 & 5 & 9 & 9 & 10 & 9 & 7 & 8 \\ 11 & 11 & 10 & 1 & 9 & 12 & 11 & 10 & 6 & 9 & 10 & 10 \\ \hline \end{tabular} A. A Type I error would be to conclude that the true mean number of solder joints inspected is not equal to 10 wh B. A Type I error would be to conclude that the sample mean number of solder joints inspected is greater than 10 C. A Type I error would be to conclude that the true mean number of solder joints inspected is less than 10 when, D. A Type I error would be to conclude that the true mean number of solder joints inspected is equal to 10 when, $\square$ Now identify what a Type II error is for this situation. Choose the correct answer below. A. A Type II error would be to conclude that the true mean number of solder joints inspected is 10 when, in fact, the mean is less than 10. B. A Type II error would be to conclude that the true mean number of solder joints inspected is less than 10 when, in fact, the mean is equal to 10. C. A Type II error would be to conclude that the true mean number of solder joints inspected is not equal to 10 when, in fact, the mean is equal to 10. D. A Type II error would be to conclude that the sample mean number of solder joints inspected is 10 when, in fact, the mean is greater than 10. c. Conduct the hypothesis test you described in part a and interpret the test's results in the context of this exercise. Use $\alpha=0.05$. Calculate the value of the test statistic. $z=\square$ $\square$ (Round to two decimal places as needed.)
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Solution

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Solution Steps

Step 1: Sample Statistics

The sample data provided yields the following statistics:

  • Sample Mean: \[ \bar{x} = 9.125 \]
  • Sample Standard Deviation: \[ s = 2.1598 \]
  • Sample Size: \[ n = 48 \]
Step 2: Standard Error Calculation

The Standard Error (\(SE\)) is calculated as follows: \[ SE = \frac{s}{\sqrt{n}} = \frac{2.1598}{\sqrt{48}} \approx 0.3117 \]

Step 3: Hypothesis Testing

The hypotheses for the test are defined as:

  • Null Hypothesis (\(H_0\)): \[ \mu = 10 \]
  • Alternative Hypothesis (\(H_a\)): \[ \mu \neq 10 \]
Step 4: Test Statistic Calculation

The test statistic (\(Z_{test}\)) is calculated using the formula: \[ Z_{test} = \frac{\bar{x} - \mu_0}{SE} = \frac{9.125 - 10}{0.3117} \approx -2.8068 \]

Step 5: P-value Calculation

For a two-tailed test, the P-value is calculated as: \[ P = 2 \times (1 - T(|z|)) \approx 0.005 \]

Step 6: Decision Rule

Given the significance level \(\alpha = 0.05\):

  • Since \(P < 0.05\), we reject the null hypothesis.

Final Answer

The sample data refute the manufacturer's claim. Thus, the conclusion is: \[ \boxed{\text{Reject } H_0} \]

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