Given Information:
The proportion of electric cars sold in 2012 = p₁ = 0.1%
The proportion of electric cars sold in 2016 = p₂ = 0.5%
Sample size of electric cars in 2012 = n₁ = 10,000
Sample size of electric cars in 2016 = n₂ = 20,000
Confidence level = 95%
Required Information:
Change in the proportion of electric cars sold from 2012 to 2016 = ?
Answer:
Change in the proportion of electric cars sold from 2012 to 2016 = (0.284%, 0.516%)
Step-by-step explanation:
The change in the mean is given by
[tex]\mu = p_2 - p_1\\\\\mu = 0.005 -0.001\\\\\mu = 0.004\\\\[/tex]
The change in standard error is given by
[tex]SE = z\cdot\sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2} }[/tex]
Where z is the value of z-score corresponding to 95% confidence level.
[tex]z_{\alpha/2} = 1 - 0.95 = 0.05/2 = 0.025\\\\z_{0.025} = 1.96\\\\[/tex]
[tex]SE = 1.96\cdot\sqrt{\frac{0.001(1 - 0.001)}{10,000} + \frac{0.005(1 - 0.005)}{20,000} } \\\\SE = 1.96\cdot 0.00059\\\\SE = 0.00116\\\\[/tex]
The change in the proportion of electric cars is
[tex]\mu \pm SE \\\\0.004\pm 0.00116 \\\\(0.004-0.00116) \: and \: (0.004-0.00116)\\\\(0.00284, \: 0.00516)\\\\(0.284\%, \: 0.516\%)[/tex]
Therefore, we are 95% confident that the change in the proportion of electric cars sold from 2012 to 2016 is between (0.284%, 0.516%)
