Question

The percentage of adults who currently play chess (at least once during the past year) is 12% in the UK. Suppose that in a random sample of n = 400 UK residents, 67 of them play chess. What is the population parameter? What is the sample statistic

Answer 1

Answer:

p represent the population parameter , true proportion of people who play chess in the UK

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

$z=\frac{0.1675 -0.12}{\sqrt{\frac{0.12(1-0.12)}{400}}}=2.923$  

Step-by-step explanation:

Data given and notation

n=400 represent the random sample taken

X=67 represent the people who play chess

$\hat p=\frac{67}{400}=0.1675$ estimated proportion of people who play chess

$p_o=0.12$ is the value that we want to test

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)  

p represent the population parameter , true proportion of people who play chess in the UK

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion i higher than 0.13.:  

Null hypothesis:$p \leq 0.12$  

Alternative hypothesis:$p > 0.12$  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$.

Calculate the statistic  

Since we have all the info required we can replace in formula (1) like this:  

$z=\frac{0.1675 -0.12}{\sqrt{\frac{0.12(1-0.12)}{400}}}=2.923$