The average breaking strength of steel rods is required to be at least 35,000 psi. Based on historical information, the standard deviation of breaking strength is 1,500 psi. A random sample of 4 specimens had the strength: piece one was 32,000, piece two was 36,000, piece three was 34,000, and piece four was 34,500. Which of the following hypothesis tests would you conduct?a.One sample t Testb.One sample Chi-square Testc.One sample Z Testd.One sample F TestClear my choice
Question
The average breaking strength of steel rods is required to be at least 35,000 psi. Based on historical information, the standard deviation of breaking strength is 1,500 psi. A random sample of 4 specimens had the strength: piece one was 32,000, piece two was 36,000, piece three was 34,000, and piece four was 34,500. Which of the following hypothesis tests would you conduct?a.One sample t Testb.One sample Chi-square Testc.One sample Z Testd.One sample F TestClear my choice
Solution
To determine which hypothesis test to conduct, we need to consider the following:
- The sample size is small (n = 4).
- The population standard deviation is known (σ = 1,500 psi).
- We are testing the mean breaking strength against a known value (35,000 psi).
Given these conditions, the appropriate test is:
c. One sample Z Test
Here's the reasoning:
- The sample size is small, but the population standard deviation is known, which makes the Z Test appropriate.
- The t Test is typically used when the population standard deviation is unknown and the sample size is small.
- The Chi-square Test is used for categorical data or for testing variances, not means.
- The F Test is used to compare two variances, not for testing a single mean against a known value.
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