To test if the process of producing ball bearings is 'out of control', we can conduct a hypothesis test using Excel's functions. Here are the steps to follow: State the null and alternative hypotheses, calculate the sample mean and standard deviation, calculate the test statistic, determine the critical value or p-value, and make a decision based on the critical value or p-value.
To test if the process of producing ball bearings is 'out of control', we can conduct a hypothesis test using Excel's functions. Here are the steps to follow:
- State the null and alternative hypotheses. In this case, the null hypothesis (H0) is that the average diameter of ball bearings is 0.500 mm, and the alternative hypothesis (Ha) is that the average diameter differs from 0.500 mm.
- Calculate the sample mean and standard deviation using the data provided. In this case, the sample mean is the average of the random sample of 36 ball bearings, and the sample standard deviation is the standard deviation of the sample.
- Calculate the test statistic, which is the difference between the sample mean and the hypothesized population mean (0.500 mm in this case), divided by the standard deviation of the sample. This is typically done using Excel's t-test function.
- Determine the critical value or p-value. At a 0.01 level of significance, we can compare the test statistic to the critical value from the t-distribution with (n-1) degrees of freedom, or calculate the p-value using Excel's t-test function.
- Make a decision. If the test statistic exceeds the critical value or the p-value is less than the significance level (0.01 in this case), we reject the null hypothesis and conclude that the process is 'out of control', indicating a significant difference in the average diameter of the ball bearings produced.