The Glen Valley Steel Company manufactures steel bars. If the production process is working properly, it turns out steel bars with mean length of at least 2.8 feet. The quality control manager wants to determine whether the production equipment needs to be adjusted. A sample of 25 bars is selected from the production line. The sample indicates a mean length of 2.73 feet, with a sample standard deviation of 0.20 feet. Should adjustments be made to the equipment? Test at the 95% confidence level.

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Chapter1: Combinatorial Analysis
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For these problems you should complete the 8 steps of the hypothesis testing process.
State the null and alternative hypotheses.
Specify alpha (a) based on the confidence level indicated.
Use alpha to develop the critical value that delineates the rejection region. Remember to use a/2
for two-tailed tests. Draw the curve and indicate the rejection region.
Use information from the problem to compute the test statistic
Calculate P-value based on test statistic.
1.
2.
3.
4.
5.
a) If population standard deviation or proportion use Z or normal distribution table
One tail: 0.5 – area in non cum table.
Two tailed: PV = 2* (0.5- area in non cum table)
b) If sample standard deviation use t table with df = n-1.
PV will be a range..e.g. 0.025 to 0.05.
Compare the test statistic to the critical value. Compare the P-value to alpha.
Based on your comparisons identify your decision (i.e. reject null hypothesis Ho or fail to reject
null hypothesis Ho). Reject the null hypothesis if the test statistic is in the rejection region.
Reject the null hypothesis if the P-value is smaller than alpha. The outcome of the p-value and
critical value approach will always lead to the same decision.
Indicate the conclusion for the scenario
6.
7.
8.
IF Reject Ho: at % (confidence level indicated) can conclude Ha
IF Fail to Reject Ho: at % (confidence level indicated) can NOT conclude Ha
Transcribed Image Text:For these problems you should complete the 8 steps of the hypothesis testing process. State the null and alternative hypotheses. Specify alpha (a) based on the confidence level indicated. Use alpha to develop the critical value that delineates the rejection region. Remember to use a/2 for two-tailed tests. Draw the curve and indicate the rejection region. Use information from the problem to compute the test statistic Calculate P-value based on test statistic. 1. 2. 3. 4. 5. a) If population standard deviation or proportion use Z or normal distribution table One tail: 0.5 – area in non cum table. Two tailed: PV = 2* (0.5- area in non cum table) b) If sample standard deviation use t table with df = n-1. PV will be a range..e.g. 0.025 to 0.05. Compare the test statistic to the critical value. Compare the P-value to alpha. Based on your comparisons identify your decision (i.e. reject null hypothesis Ho or fail to reject null hypothesis Ho). Reject the null hypothesis if the test statistic is in the rejection region. Reject the null hypothesis if the P-value is smaller than alpha. The outcome of the p-value and critical value approach will always lead to the same decision. Indicate the conclusion for the scenario 6. 7. 8. IF Reject Ho: at % (confidence level indicated) can conclude Ha IF Fail to Reject Ho: at % (confidence level indicated) can NOT conclude Ha
Problem 7:
The Glen Valley Steel Company manufactures steel bars. If the production process is working properly, it
turns out steel bars with mean length of at least 2.8 feet. The quality control manager wants to determine
whether the production equipment needs to be adjusted. A sample of 25 bars is selected from the production
line. The sample indicates a mean length of 2.73 feet, with a sample standard deviation of 0.20 feet. Should
adjustments be made to the equipment? Test at the 95% confidence level.
Transcribed Image Text:Problem 7: The Glen Valley Steel Company manufactures steel bars. If the production process is working properly, it turns out steel bars with mean length of at least 2.8 feet. The quality control manager wants to determine whether the production equipment needs to be adjusted. A sample of 25 bars is selected from the production line. The sample indicates a mean length of 2.73 feet, with a sample standard deviation of 0.20 feet. Should adjustments be made to the equipment? Test at the 95% confidence level.
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