Question

A software company decided to conduct a survey on customer satisfaction. Out of 564 customers who participated in the online survey, 51 rated the overall services as poor. Test, at level , the null hypothesis that the proportion of customers who would rate the overall car rental services as poor is 0.1 versus a two-sided alternative. Find the value of the test statistic (round off to first decimal place).

Answer 1

Answer:

$z=\frac{0.0904 -0.1}{\sqrt{\frac{0.1(1-0.1)}{564}}}=-0.760 \approx -0.8$  

$p_v =2*P(z$  

Step-by-step explanation:

Information given

n=564 represent the sample selected

X=51 represent the number of people who rated the overall services as poor

$\hat p=\frac{51}{564}=0.0904$ estimated proportion of people who rated the overall services as poor  

$p_o=0.1$ is the value to compare

z would represent the statistic

Hypothsis to analyze

We want to analyze if the proportion of customers who would rate the overall car rental services as poor is 0.1, so then the system of hypothesis are:  

Null hypothesis:$p=0.1$  

Alternative hypothesis:$p \neq 0.1$  

The statistic for a one z test for a proportion is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)  

Replacing the info given we got:

$z=\frac{0.0904 -0.1}{\sqrt{\frac{0.1(1-0.1)}{564}}}=-0.760 \approx -0.8$  

And the p value since we have a bilateral test is given b:

$p_v =2*P(z$