From past experiences, Prof. A believes that the average score on final exam is 75. A sample of 20 students’ exam scores is as follows: 80, 68, 72, 73, 76, 98, 71, 71, 35, 50, 63, 71, 70, 70, 76, 75, 69, 70, 72, 74
Assuming a normal population, can we conclude that the students’ average is still 75? Use alpha = 0.01
a. If Prof. A used every other student on the class list, what type of samplingwas used?
b. Use minitab to construct any graphs that might help you describe the distribution of this dataset. Comment on skewnessor symmetry, and gaps (if any).
c. Give the Five-Point summary, the mean, and the standard deviationfor this data set and decide if this data set is best described by the mean and standard deviation or by the five-point summary.
d. For the situation described here, identify the population and the sample.
e. Check the normality of this data set and explain.
f. Discuss the relative position of the mean, median, and modefor this data set and explain.
g. Does this data set contain any outliers? Explain.
h. Identify the numerical values of the assumed parameters and the statisticsfor the mean and standard deviation in this problem. If a parameter is unknown, write unknown.
i. At 95% confidence level, find the confidence intervalfor the mean.
j. What is the error of estimate?
k. What will happen to the width of the confidence interval if the sample size is increased to 29?
l. What will happen to the width of the confidence interval if the level of confidence is increased to 99%?
m. If 200 samples are collected, what does a 95% confidence level tell you?
n. Is there enough evidence to reject Prof. A’s belief at  = 0.05?
State the hypothesis Ho :
o. Find the critical, test value, and the p-value:
p. State your conclusion within the context of the problem:
q. Classify items in sections b, c, i, and n as pertinent to descriptive statisticsor inferential statistics.
The solution provides step by step method for statistical analysis in Minitab . Formula for the calculation and Interpretations of the results are also included.