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- Apr 14, 2013

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A public transport company claims that its buses are at least $95\%$ on time. (A bus is still on time here, if he has at most $3$ minutes delay compared to the timetable.) A sample size of $n = 1000$ at various stops results in $66$ delays. The probability that a randomly selected bus will arrive on time is denoted by $p$.

(a) You as a passenger doubt the claim of the enterprise. Test the company's claim to a significance level of $\alpha = 0, 10$.

(b) Use an example to explain the second-type error.

I have done the following:

(a) The null hypothesis is $H_0: p\geq 95\%$. The alternative hypothesis is therefore $p<95\%$. The rejection area is $\overline{A}=\{0, \ldots , k\}$ and the acceptance is $\{k+1, \ldots , 1000\}$.

From the significance level we have that $P(X\leq k)\leq 0.10\Rightarrow F(1000, 95, k)\leq 0.10$, right? I haven't really understood how we can read from a table the value of $k$. Could you explain it to me?