Question

The time (minutes) taken for a technician to complete routine maintenance on two different machines is given below:

Machine 1 = {15, 20, 11, 23, 16, 21, 18, 16, 27, 24}
Machine 2 = {23, 31, 13, 19, 23, 17, 28, 26, 25, 28}
Test the hypothesis that the mean maintenance time for machine 1 is less than that of machine

Answer 1

To test the hypothesis that the mean maintenance time for machine 1 is less than machine 2, we can use a one-sample t-test. This involves defining the null and alternative hypothesis, calculating the sample means and standard deviations, calculating the t-statistic, finding the critical value, and interpreting the results.

Step-by-step explanation:

This question is related to hypothesis testing for means. To test the hypothesis that the mean maintenance time for machine 1 is less than that of machine 2, we can use a one-sample t-test. Here are the steps:

1. Define the null and alternative hypothesis:
   Null hypothesis (H0): The mean maintenance time for machine 1 is greater than or equal to machine 2. Alternative hypothesis (Ha): The mean maintenance time for machine 1 is less than machine 2.
2. Calculate the sample means for machine 1 and machine 2.
3. Calculate the sample standard deviations for machine 1 and machine 2.
4. Calculate the t-statistic using the formula: t = (mean1 - mean2) / √((s12)/n1 + (s22)/n2), where mean1 and mean2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
5. Find the critical value for the desired significance level and degrees of freedom. Compare the t-statistic to the critical value to determine if the null hypothesis should be rejected.
6. Interpret the results and conclude whether there is evidence to support the hypothesis that the mean maintenance time for machine 1 is less than machine 2.