Test between Means of Two Samples - TOPIC!!!

1 An agriculturist would like to compare the yields of two varieties of rice (A and B) subjected to the same conditions. 10 hectares were planted with variety A and yielded an average of 80 sacks/hectare with a standard deviation of 6 sacks/hectare. 15 hectares were planted with variety B and yielded 75 sacks /hectare with a standard deviation of 8 sacks/hectare. Is variety A better than variety B at 10% level of significance?

2 The mean weekly earnings of a sample of 48 mall employees is Php 6,200, with a standard deviation of Php 152. The mean weekly earnings of a sample of 23 office employees is Php 6,800, with a standard deviation of Php 180. Is it reasonable to say that there is not a significant difference in the pay between mall employees and office employees at 10% level of significance?

3. According to a certain survey at the time of COVID-19 lock down, 60% of 33 workers from Barangay Tabuco and 55% of 40 workers from Barangay Dinaga lost their jobs. Is there a significant difference between the proportion of workers who lost their jobs coming from these two barangays at 1% significance level?

4 A researcher wants to examine the possibility that women are more likely to commit suicide off a cliff than men are. Data from the past 5 years show that out of 987 men who committed suicide, 394 jumped off a cliff. On the other hand, 44% of the 500 women who committed suicide did so by jumping off a cliff. What can be said about the researcher's claim at 5% level of significance?