(a)[1]
State the probability of a Type I error.
(b)[5]
Assume that after $2004$, the value of $\sigma$ remains $6.95$. If the actual value of $\mu$ this year is $164.91$, find the probability of a Type II error.
Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The heights, in centimetres, of adult females in Litania have mean $\mu$ and standard deviation $\sigma$. In 2004, the respective values of $\mu$ and $\sigma$ were $163.21$ and $6.95$. The government states that this year’s value of $\mu$ is higher than the 2004 figure. To check this statement, a researcher intends to perform a hypothesis test at the $1\%$ significance level. He measures the heights of a random sample of $300$ adult females in Litania this year and obtains the sample mean.