Weinstein, McDermott, and Roediger report that students who were givne questions to be answered while studying new material had better scores when tested on the material compared to students who were simply given an opportunity to reread the material. In a similiar study, an instructor in a large psychology class gave one group of students questions to be answered while studying for the final exam. The overall average for the exam was mean = 73.4, but the n = 16 students who answered questions had a mean of M =78.3 with a standard deviation of s=8.4. For this study, did answering questions while studying produce significantly higher exam scores? Use a one tailed test with alpha = .01.

Answer with explanation:Let [tex]\mu[/tex] be the population mean.By considering the given information , we have Null hypothesis : [tex]H_0: \mu=73.4[/tex]Alternative hypothesis :  [tex]H_a: \mu>73.4[/tex]Since alternative hypothesis is right-tailed , so the test is a right-tailed test.Given : Sample size : n=16 , which is a small sample , so we use t-test.Sample mean: [tex]\overline{x}=78.3[/tex]  ;Standard deviation: [tex]s=8.4[/tex]Test statistic for population mean:[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]i.e. [tex]t=\dfrac{78.3-73.4}{\dfrac{8.4}{\sqrt{16}}}\approx2.333[/tex]Using the standard normal distribution table of t , we haveCritical value for [tex]\alpha=0.01[/tex] : [tex]t_{(n-1,\alpha)}=t_{(15,0.01)}=2.602[/tex]Since , the absolute value of t (2.333) is smaller than the critical value of t (2.602) , it means we do not have sufficient evidence to reject the null hypothesis.Hence, we conclude that we do not have enough evidence to support the claim that answering questions while studying produce significantly higher exam scores.