Perform a hypothesis test at the α = 0.05 level testing whether the average cumulative GPA in
the upper-level statistics course is greater than 3.0. a.
List the null and alternative hypotheses: The null hypothesis would be Ho: μ < 3 and the Alternative hypothesis is Ho: μ > 3
b.
Compute a z or t statistic for this hypothesis test (whichever one is appropriate): Sample Mean = 3.2467, Sample Standard Deviation = 0.534, Sample Size = 30. T Statistic = Sqrt 30 (3.2467 -3)/0.536 = 2.529 c. Compute the p-value: P-value = P[t29 > 2.529] = .008 < 0.05 d. What do you conclude from your hypothesis test? Is the average GPA in the class greater than 3.0? Since P-value < 0.05, We Reject Ho, as the data we gathered provides enough evidence to show that the population mean cumulative GPA is greater than 3 e. Define what a p-value is in two sentences or less. The P-value is a measurement to help make sure our hypothesis is considered valid compared to the observed data. 2. Perform a hypothesis test at the α = 0.05 level testing whether fewer than half of the student's
earned semester honors the previous semester. a.
Compute the proportion of students that received semester honors last semester. (The functions = COUNTIF () in Excel and which () in R may be helpful). D = 0.05, number of students = 30, number o b. Compute a z or t statistic for this hypothesis test (whichever one is appropriate): 0.4 - 0.5 / Sqrt 0.5*0.5 /30 = -0.1/0.091287 = -1.095 c.
Compute the p-value: The P-value = 0.136758 d.
What do you conclude from your hypothesis test? Did fewer than half of the students in the course receives semester honors? We do not reject the null hypothesis, The true population proportion of students that have earned honors is 0.5 which P = 0.
