Question

A research group wants to determine whether the proportion of car accidents that were caused by drivers using cell phones has changed from the previous value of 13%. They obtained 10,000 auto accident reports and found that 14% were caused by drivers using cell phones. Find the test statistic.

Answer 1

Answer: -2.88

Step-by-step explanation:

Hypothesis : The proportion of car accidents that were caused by drivers using cell phones has changed from the previous value =13%

i.e. p=0.13

Sample size : $10,000$

The proportion of auto accident were caused by drivers using cell phones.

$P=0.14$

Now, the test statistic for the population proportion is given by :-

$z=\dfrac{p-P}{\sqrt{\dfrac{P(1-P)}{n}}}$

$\Rightarrow\ z=\dfrac{0.13-0.14}{\sqrt{\dfrac{0.14(1-0.14)}{10000}}}\Rightarrow\ z=-2.881952088\approx-2.88$

Hence, the value of the test statistic is -2.88