The multi-part question is worth 6 marks (1 mark per sub-part) andincludes both numerical and written answers. For numerical answers,calculationswhen requestedand do not round answers (railing zeros are not required). For written questions, typeone wordonly.

During the winter semester, students obtained, on average, a score of 78 with a standard deviation of 42 on a midterm exam. The professor was interested to know whether grades would significantly change during the summer semester due to the ease of restrictions. Therefore, she chose a random sample of 49 students registered in the summer semester and had them take the same exam.

a.State the null hypothesisin symbols.H₀:Answer

b. State the alternative hypothesisin symbols. H₁:Answer

c.Students from the summer semester obtained a mean score of 90. Calculate z_obs. First, write your calculation:Answer. Then, write your answer:Answer

d.What p-value is associated withz_obs?Please, write 4 decimal points.p =Answer

e.If we adopt the p < .05 significance level, isthe p-valuestatistically significant?(yes/no) Answer

f.Should you retain or rejectH₀?(retain/reject) Answer