Question

Design and analysis of experiments

Case of the winder in the company GOMAR Electrica in Querétaro and Salamanca - Gomar is a trader of electrical material when cutting cable lengths with a winder, ensures that the average of its measurement and cutting process is at nominal. - The target length to test his hypothesis is 50 cm. - Analyze the sample with a t-test - Is the supplier Gomar right?
- Consider a = .05.
Lengths: 50.96 52.36 48.01 53.99 54.33 49.94 61.66 51.51 56.67 55.81 53.05 55.86 54.97 54.02 50.90.
Conclusions:
Given that:
(a) The value of the test statistic is ______ than the critical value _______ ,

Answer 1

To assess the cable lengths cut by GOMAR Electrica, a t-test is used to determine if the lengths significantly deviate from 50 cm. The test statistic is compared with the critical value to decide whether to reject the null hypothesis. Correct calculations are essential for accurate conclusions.

Step-by-step explanation:

The student has asked for help with performing a t-test for a hypothesis test regarding the average cable lengths cut by a winder in the company GOMAR Electrica. With a target length of 50 cm, we use a t-test to determine if the actual lengths are significantly different from the hypothesis.

To carry out the t-test, we would first need to calculate the sample mean and standard deviation based on the provided lengths. We would then set up our null hypothesis (H0): that the mean length is 50 cm, against the alternative hypothesis (Ha): that the mean length is not 50 cm. With a significance level (α) of 0.05, we compare the calculated t statistic to the critical value from the t-distribution to determine if we should reject the null hypothesis or fail to reject it.

The test statistic would be compared to the critical value for the degrees of freedom associated with our sample size. If the absolute value of the test statistic is greater than the critical value, we would reject the null hypothesis and conclude that GOMAR's cable cutting process does not produce an average length of 50 cm. Conversely, if the test statistic is less than the critical value, we would fail to reject the null hypothesis.

It's worth noting that correct calculations are crucial for the interpretation of the t-test and to determine if Gomar's assertion about their process is accurate.