A student believes that the average grade on the statistics final examination is 88. A sample of 36 final examinations is taken. The average grade in the sample is 83.96. The population variance is 144. a. Conduct a hypothesis test to determine whether the average grade on the statistics final examination is 88. Use = .03 for the level of significance. (a1) Formulate the null and alternative hypotheses that can be used to determine whether the average grade on the statistics final examination is 88. (fill in the blanks below). [2 pts] H0 = ____________ Ha = ____________ (a2) What is the test statistic? [4 pts] (a2.1) Write down the formula calculating the test statistic: _____________________________________ (a2.2) Start your calculation here: _________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________ (a3) What is the p-value? (If you use Excel, provide the function you use) [5 pts] ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________ (a4) What is the critical value based on = 0.03? (If you use Excel, provide the function you use) [5 pts] ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________ (a5) Use = 0.03. Provide the result of the hypothesis test. (5.1) What is the rejection rule you use for the hypothesis test? [1 pt] ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________ (5.2) Do you reject or not reject H0? [1 pt] ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________ (5.3) What is your conclusion? Interpret the meaning of the conclusion. [2 pt] ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________ b. Given that the population has a normal distribution, develop a 95% confidence interval for the population mean grade on the statistics final examination. (b1) What is the point estimate? [2 pts] ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________ (b2) What is the standard error of the mean? [2 pts] ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________ (b3) What is the margin of error? [2 pts] ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________ (4) What is the 95% confidence interval estimation? [2 pts] ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _____________________ c. Using the 95% confidence interval estimate from part b, conduct a hypothesis test to determine whether the average grade on the statistics final examination is 88. What is your conclusion? Use = .05 for the level of significance. [5 pts] ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _______________________________________________________