## Week Five Quiz >>> In the jury version of hypothesis testing the alternative hypothesis is >>> Probability and Statistics: To p or not to p?

### 1.

Question 1

In the jury version of hypothesis testing, the alternative hypothesis is

H1: not guilty

H1: guilty

### 5.

Question 5

If the $p$-value for a test was 0.07 and $α=0.05$, the appropriate decision is:

reject H0 at the 5% significance level

accept H0 at the 5% significance level

not reject H0 at the 5% significance level

reject H1 at the 5% significance level

### 8.

Question 8

Under the central limit theorem, when sampling from non-normal distributions the distribution of $Xˉ$ tends to:

a normal distribution with mean $μ$ and variance $σ_{2}$, as $n→∞$

a normal distribution with mean $μ$ and variance $σ_{2}/n$, as $n→∞$

### 9.

Question 9

When sampling from a Bernoulli distribution, the sample proportion, $P$, has:

E(P)=π and Var(P)=π(1−π)

E(P)=π and Var(P)=π(1−π)/n

### 10.

Question 10

When performing a hypothesis test of a single proportion, we use the test statistic:

$p(−p)n P−π ∼N(0,1)$

$π(−π)n P−π ∼N(0,1)$

### 1.

Question 1

In the jury version of hypothesis testing, the null hypothesis is:

H0: not guilty

H0: guilty

### 2.

Question 2

In hypothesis testing, a Type I error is:

rejecting H0 when H0 is true

not rejecting H0 when H0 is false.

### 4.

Question 4

In general, we test at the $100α$% significance level, for $α∈[0,1]$ such that we control for the:

probability of a Type I error

probability of a Type II error

### 7.

Question 7

If a hypothesis test does not reject H0, then which of the following might have occurred?

A Type I error

A Type II error

### 9.

Question 9

The sampling distribution of the sample proportion, $P$, is:

$N(π,π(1−π)/n)$ for any $n$

$N(π,π(1−π)/n)$ as $n→∞$

### 3.

Question 3

In hypothesis testing, the conditional probability P(H0 not rejected|H0 is true)=

$α$

$β$

1−α

1−β

### 4.

Question 4

In general, we control for the probability of a Type I error by choosing:

**\alpha [0, 1 and so test at the $100α$% significance level**