Question

At most 42% of car crashes occur within 2 miles of the motorists home. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage). H 0 : p =42% Correct H 1 : p >=42% Incorrect Use the following codes to enter the following symbols: ≥ enter >= ≤ enter <= ≠ enter !=
Part B)You are performing a two-tailed test. If α = .001 , find the positive critical value, to three decimal places. zα/2 =

Answer 1

Answer:

A)$H_{0}: p \leq 0.42\\H_A: p > 0.42$

B)

$z_{critical} \text{ at 0.001 level of significance } = \pm 3.291$

Step-by-step explanation:

A) We are given the following in the question:

At most 42% of car crashes occur within 2 miles of the motorists home

p = 42% = 0.42

We design the null and the alternate hypothesis  in the following manner:

$H_{0}: p \leq 0.42\\H_A: p > 0.42$

At most 42% of car crashes occur within 2 miles of the motorists home which means car crashes should be less than equal to 42% but not greater than 42%.

The null hypothesis sates that 42% or less car crashes occur within 2 miles of the motorists home.

The alternate hypothesis state that more than 42% of car crashes occur within 2 miles of the motorists home.

B) We have to find the value of z critical for given conditions

We are performing a two tailed test.

Alpha, α = 0.001

Calculating the z value from the standard z-table. We find the value from the table under the level of significance 0.001

The value obtained is used as the acceptance region for the null hypothesis.

The obtained acceptance region can be written as:

$z_{critical} \text{ at 0.001 level of significance } = \pm 3.291$

If the calculated z score lies in this region we accept the null hypothesis. If not we reject the null hypothesis.