Answer to Question #213031 in Statistics and Probability for Daniel

Question

The director of a certain school for secretarial studies claimed that his graduates can type more than 85 words per minute. A random sample of 15 graduates has been found to have an average of 80 words per minute with a standard deviation of 7.6 words per minute. Using 0.05 level of significance, test the claim of the director.

Answer 1

$H_0:\mu=85$

$H_a:\mu>85$

$\bar X=80$

$s=7.6$

$n=15$

Assume that the data follow a normal distribution. Since population standard deviation is unknown, t-score is used.

$t=\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}$

$=\frac{80-85}{\frac{7.6}{\sqrt{15}}}$

$-2.548$

$cv=t_{0.05,14}$

$=1.761$

The test statistic is less than the critical value (right tailed test), we fail to reject the null hypothesis. There is no sufficient evidence to support the claim that graduates can type more than 85 words per minute.