Reference no: EM131736799

The Department of Social Sciences wants to examine the student's grade for a course . A random sample of 10 students currently taking SC101 is selected, and their mid-term test scores are obtained as follows. From past academic records, the population standard deviation is known to be 5.6 marks.  

Observation  1  2  3  4  5  6  7  8  9  10 

Test Score 65  80  52  89  72   90  76  72  96  88

In additional to the above 10 selected students, 30 more students are randomly selected. Among the 30 newly selected students, 80% of them passed the mid-term test (passing mark is 50).  

1) Do these 40 selected students provide evidence that more than 70% of SC101 students passed the mid-term test? Using p-value approach, conduct a hypothesis test at 10% level of significance. Verify the three conditions for normal approximation.