Question

# A professor wants to know if her introductory statistics class has a good grasp of basic...

A professor wants to know if her introductory statistics class has a good grasp of basic

math. Six students are chosen at random from the class and given a math proficiency

test. The six students score a sample average of 60.83 with a sample standard deviation of 13.17. Can the professor conclude that the mean score for the class on the test would

be below 70? Use a significance level of 0.05

Hypothesis: Vs

Since the population standard deviation is not known.

Therefore , use t-distribution.

Now , df=degrees of freedom-n-1=6-1=5

Therefore , the critical value is ,

The test statistic is ,

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject Ho.

Conclusion : Hence , there is not sufficient evidence to conclude that the the mean score for the class on the test would be below 70.

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