Question

Dean suspects that statistics teacher increase the grades of the class of 75 students due to his endless love to his beloved students. Dean realized that average grade of previous statistics classes is 64 and she took some of the exams from student affairs departments and note the following grades: 65 75 98 34 76 52 80 84 68. Please help dean to conduct a statistical analysis and (15 points) interpret the results. (15 points)

Answer 1

For analysing the data here we want to test whether the statistics teacher increase the grades of the class.

Let be the average of grades of the class.

Therefore the test hypothesis is given as

The null hypothesis is given as

i.e the average of grades of the class is 64

vs the alternative hypothesis is

i.e the average of grades of the class is more than 64.

The random sample of grades is given as

65 ,75 ,98 ,34 ,76 ,52 ,80 ,84 ,68

n=6

Obtaining the sample mean

= 632/9

=70.2222

Obtaining the sample standard deviation

=348.6944

s=  18.67336

The test statistic is given as

=0.9996057

Rounding to four decimal

= 0.9996

The degree of freedom is

df= n-1

=8

Obtaining the p-value with df =8 and t= 0.9996

P[ t₈ > 0.9996 ] =  0.8266122

At 5% level of significance

p-value > 0.05

Hence we failed to reject the null hypothesis.

There is no sufficient evidence to conclude that statistics teacher significance increase the grades of the class .