A manufacturer uses a new production method to produce steel rods. A random sample of 27 steel rods resulted in lengths with a standard deviation of 3.89 cm. At the 0.01 significance level, using the p-value method, test the claim that the new production method has lengths with a standard deviation different from 3.61 cm, which was the standard deviation for the old method.

A lumber company is making boards that are 2599.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 23 is made, and it is found that they have a mean of 2600.3 millimeters with a standard deviation of 13.0 A level of significance of 0.05 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.

In a study of pulse rates of men, a simple random sample of 150 men results in a standard deviation of 11.4 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute; see the accompanying StatCrunch display for this test. What do the results indicate about the effectiveness of using the range rule of thumb with the "normal range" from 60 to 100 beats per minute for estimating o in this case? Assume that the simple random sample is selected from a normally distributed population. Click the icon to view the StatCrunch display. Let o denote population standard deviation of the pulse rates of men (in beats per minute). Identify the null and alternative hypotheses. Ho: o H₁:…

A children’s clothing company sells hand-smocked dresses for girls. The length of one particular size of dress is designed to be 3939 inches. The company regularly tests the lengths of the garments to ensure quality control, and if the mean length is found to be significantly longer or shorter than 3939 inches, the machines must be adjusted. The most recent simple random sample of 2929 dresses had a mean length of 36.8936.89 inches with a standard deviation of 7.567.56 inches. Assume that the population distribution is approximately normal. Perform a hypothesis test on the accuracy of the machines at the 0.0250.025 level of significance.   Step 2 of 3 :   Compute the value of the test statistic. Round your answer to three decimal places.   step 3of 3 :  Conclusion - Reject the null hypothesis/ fail to reject ...insufficient/sufficient