stats Assignment

A sample of Exam 1 grades from an English 101 course of 37 students was collected in order to analyze the validity of the instructor’s claim that all students pass Exam 1 with a C or better. The sample consisted of 10 A’s (27%), 11 B’a (33%), 3 C’s (8%), 8 D’s (22%), and 5 F’s (14%). The pie graph below illustrates the composition of grades for Exam 1. The average grade on Exam 1 for the 37 students was 77.81 with a standard deviation of 18.05.

The appropriate statistical test that should be used in this case is the Student’s t-test since population standard deviation (σ) is unknown and sample standard deviation is used an estimate of σ. The significance level will be assumed to be 0.05. The null hypothesis is that the average Exam 1 grade is at most a C (i.e. no larger than a 70). This hypothesis is tested against the claim that the average Exam 1 grade is greater than a C (i.e. larger than 70). In other words, following set of hypotheses are being tested: vs .

Next, a test statistic is calculated using the t-test formula: . Correctly evaluating this equation results in a t-value of 2.63. In order to make a statistical decision, the test statistic (t= 2.63) must be compared to the corresponding critical values that depend on α and degrees of freedom (df). With α = 0.05 and , the critical value for this right tailed test is 1.688. Therefore, the null hypothesis can be rejected whenever . For this analysis, the test statistic of 2.63 exceeds the critical value of 1.688 (). Thus, the null hypothesis is rejected and it can be concluded that the alternative hypothesis is true. There is sufficient evidence at the 0.05 level that average grades on Exam 1 for all English 101 courses is significantly higher than a 70.0.

The distribution of this sample data was slightly skewed with more than half of the class receiving a grade of A or B. Evaluating a larger sample size may provide more accurate results, but the overall outcome would probably be the same. An interesting aspect would be to collect gender and then analyze if the average grade differs by gender. This is an interesting question an being able to interpret the results is very beneficial in the educational field.

Percentage of Grades A B C D F 0.27 0.30000000000000004 8.0000000000000016E-2 0.22 0.14000000000000001