A typist claims that he can take dictations at the rate of more than
120 words per minutes. of the 12 tests given to him , he could
perform an average of 135 words with a standard deviation of 40.
is the his claim valid. use 1% significant
To determine if the typist's claim is valid, we can conduct a one-sample t-test.
The null hypothesis (H0) is that the average typing speed is 120 words per minute.
The alternative hypothesis (H1) is that the average typing speed is greater than 120 words per minute.
Given that the sample mean (x̄) is 135 words per minute, standard deviation (s) is 40, number of tests (n) is 12, and the significance level is 1%, we can calculate the t-score as follows:
t = (x̄ - μ) / (s / √n)
t = (135 - 120) / (40 / √12)
t = 15 / (40 / 3.4641)
t = 15 / 11.6186
t = 1.2908
Now, we can compare the calculated t-score to the critical t-value. Since the alternative hypothesis is that the average typing speed is greater than 120 words per minute, we will use a one-tailed test.
Degrees of freedom (df) = n - 1 = 12 - 1 = 11
Critical t-value = 2.718 (from t-table for df = 11 and α = 0.01)
Since the calculated t-score (1.2908) is less than the critical t-value (2.718), we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the typist's claim that he can take dictations at a rate of more than 120 words per minute.