Easy -1.2 This is a straightforward recall question about the definition of Type I error. Students only need to know that the probability of Type I error equals the significance level (5%), requiring no calculation or application. The sample data and distribution details are irrelevant distractors.
2 Jamie is conducting a hypothesis test on a random variable which has a normal distribution with standard deviation 1
The hypotheses are
$$\begin{aligned}
& \mathrm { H } _ { 0 } : \mu = 5 \\
& \mathrm { H } _ { 1 } : \mu > 5
\end{aligned}$$
He takes a random sample of size 4
The mean of his sample is 6
He uses a 5\% level of significance.
Before Jamie conducted the test, what was the probability that he would make a Type I error?
Circle your answer. [0pt]
[1 mark]
\(0.0228 \quad 0.0456 \quad 0.0500 \quad 0.1587\)
2 Jamie is conducting a hypothesis test on a random variable which has a normal distribution with standard deviation 1
The hypotheses are
$$\begin{aligned}
& \mathrm { H } _ { 0 } : \mu = 5 \\
& \mathrm { H } _ { 1 } : \mu > 5
\end{aligned}$$
He takes a random sample of size 4\\
The mean of his sample is 6\\
He uses a 5\% level of significance.\\
Before Jamie conducted the test, what was the probability that he would make a Type I error?
Circle your answer.\\[0pt]
[1 mark]
$0.0228 \quad 0.0456 \quad 0.0500 \quad 0.1587$
\hfill \mbox{\textit{AQA Further Paper 3 Statistics 2020 Q2 [1]}}