Question

Researchers collected data from 100 randomly chosen counties in Texas on pollution levels and asthma rates. Pollution levels were measured by calculating the average number of air particulates (in mg/m3) and asthma rates were calculated as the percent of residents (0-100%) diagnosed with asthma. After confirming all relevant assumptions, they ran a linear model predicting asthma rates based on pollution level: Estimate Std. Error (Intercept) 3.61 2.05 pollution 0.78 0.29 Are pollution levels in Texas counties a significant linear predictor of asthma rates

Answer 1

The answer is "3.14".

Explanation:

The coefficient of pollution level is "b" and "a" intercept

`\to y=a+bx\\\\`

We must verify it.

`H_0 :\beta = 0\\\\H_a : \beta \\eq 0\\\\`

`Beta \to b=1.76, SE=0.56 \ Estimate`

The statistics on tets are now provided

`\to t=(b)/(SE)=(1.76)/(0.56)=3.14`

Because statistics will be more than critical
`(1.984)` values, we thus reject
`H_0`