Question

An oil company claims that in a fifth of the homes in a certain city people use oil as fuel to heat them. Are there reasons to believe that in less than a fifth of households people use this fuel to heat them if, in a random sample of n = 1000 households in that city, it is found that x = 170 uses oil as fuel? The test statistic would be:

a) 2.43

b) 1.72

c) -3.35

d) -2.37

Answer 1

Answer:

population proportion: p = 1/5 = 0.2

sample size: n= 1000, x= 170

sample proportion : $\hat p$ = x/ n =170 / 1000 = 0.17

formula for test statistics is

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

$z= \frac{ 0.17 -0.2 }{ \sqrt{\frac{0.2* (1-0.2)}{1000}}}$

z= -2.37

test statistics = -2.37