Question

Training hours are essential for employees, but managers were complaining that their entire team was training at the same time and therefore productivity was down. The CEO wanted to see if there was any truth to this, so she surveyed the amount of training hours each employee had in a week's time and then asked the managers how many employees they felt out of their team of 100 were at training for a specific number of minutes that week. Conduct a Chi-Square hypothesis test with a 1% level of significance.

Minutes in training Observed (O) Expected (E)
30 70 62
60 59 48
90 60 52
120 15 10


a) Record the null and alternative hypotheses.

Answer 1

The student's question is about performing a Chi-Square hypothesis test to see if the observed employee training hours agree with expected hours, with null and alternative hypotheses and comparing the calculated Chi-Square statistic to the critical value at a 1% significance level.

Step-by-step explanation:

The student's question involves conducting a Chi-Square hypothesis test to determine if the number of training hours attended by employees matches the managers' expectations. The null hypothesis (H0) is that the observed training hours match the expected hours (there is no significant difference between the observed and expected frequencies).

The alternative hypothesis (Ha) is that there is a significant difference between the observed training hours and the expected hours. To perform the test, we would use the Chi-Square formula to calculate the test statistic:

Χ² = ∑ ((O-E) ² / E)

where O represents the observed frequency and E represents the expected frequency. Then, we compare the calculated Chi-Square value to the critical value from the Chi-Square distribution table at a 1% level of significance. If the calculated value is greater than the critical value, we reject the null hypothesis. If it is smaller or equal, we do not reject the null hypothesis.