Evaluating Sample Mean Using One-Sample t-test

00:00 6 marks

A faculty member is investigating whether the average exam score of a particular course significantly differs from the national average of 70. A random sample of 25 students from the course had an average score of 72 and a sample standard deviation of 8. Using a significance level of 0.05, perform a one-sample t-test.

(a) State the null and alternative hypotheses.
(b) Calculate the t-statistic.
(c) Provide a conclusion based on the computed t-statistic and the critical value.

Hint Hint

Hint

Remember to compute the standard error as \(\frac{s}{\sqrt{n}}\) and use it to calculate the t-statistic.

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a) \(H_0: \mu = 70\), \(H_a: \mu
eq 70\).

b) t-statistic = \(\frac{72 – 70}{8/\sqrt{25}} = \frac{2}{1.6} = 1.25\).

c) With \(df = 24\) and a critical value of approximately \(\pm2.064\) at the 0.05 significance level, we fail to reject \(H_0\), indicating no significant difference.

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