Merta reports that 74% of its trains are on time. A check of 60 randomly selected trains shows that 38 of them arrived on time.
Find the probability that among the 60 trains, 38 or fewer arrive on time. Based on the result, does it seem plausible that the "on-time" rate of 74% could be correct?
The confidence interval would be more narrow if the confidence level were changed to 90%
Step-by-step explanation:
For a small sample size of n = 18 a pivotal quantity that we can use to form a confidence interval for is given by that has a t distribution with (n-1) degrees of freedom. We find a % confidence inverval using , where is the t-value such that there is an area equal to above this t-value and below the curve of the density of the t distribution with n-1 df. We find a 95% confidence interval with and we find a 90% confidence interval with . Because of and , the confidence interval would be more narrow if the confidence level were changed to 90%.