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S_A_V [24]
3 years ago
13

A mileage test is conducted for a new car model. Thirty randomly selected cars are driven for a month and the mileage is measure

d for cach. The mean mileage for the sample is 28.6 miles per gallon (mpg) and the sample standard deviation is 2.2 mpg Estimate a 95% confidence interval for the mean mpg in the entire population of that car model.
Chemistry
1 answer:
Leni [432]3 years ago
4 0

Answer:  (27.81,\ 29.39)

Explanation:

Given : Sample size : n= 30 , it means it is a large sample (n≥ 30), so we use z-test .

Significance level : \alpha: 1-0.95=0.05

Critical value: z_{\alpha/2}=1.96

Sample mean : \overline{x}=28.6

Standard deviation : \sigma=2.2

The formula to find the confidence interval is given by :-

\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

i.e. 28.6\pm (1.96)\dfrac{2.2}{\sqrt{30}}

i.e. 28.6\pm 0.787259889321

\approx28.6\pm 0.79=(28.6-0.79,28.6+0.79)=(27.81,\ 29.39)

Hence, the 95% confidence interval for the mean mpg in the entire population of that car model = (27.81,\ 29.39)

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