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11111nata11111 [884]
3 years ago
9

An automobile manufacturer has developed a new compact automobile. A random sample of 64 of the new automobiles showed that the

automobiles had a sample mean mileage of 28.75 miles per gallon and a sample standard deviation of 3.4 miles per gallon. a) Find the 95% confidence interval for the population mean mileage, and state your conclusion. b) Find the 98% confidence interval for the population mean mileage, and state your conclusion.
Mathematics
1 answer:
Firdavs [7]3 years ago
7 0

Answer:

<em>The 95% confidence interval for the population mean mileage is </em>

(27.917, 29.593)

The 98% confidence interval for the population mean mileage

(27.737, 29.762)

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given that the random sample size 'n' = 64</em>

<em>Given that the mean of sample x⁻ = 28.75miles</em>

<em>Given that the standard deviation of the sample (S) = 3.4 miles</em>

<em>Degrees of freedom = n-1 = 64-1 =63</em>

<em>t₀.₀₅ = 1.9983</em>

<u>Step(ii):-</u>

<em>95% confidence interval for the population mean mileage is determined by</em>

<em />(x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} })<em />

(28.75-1.99\frac{3.4}{\sqrt{64} },28.75 + 1.99 \frac{3.4}{\sqrt{64} } )

(28.75 - 0.845 , 28.75 + 0.845)

(27.917 , 29.593)

<u><em>Step(iii</em></u>):-

<em>98% confidence interval for the population mean mileage is determined by</em>

<em />(x^{-} - t_{0.02} \frac{S}{\sqrt{n} } , x^{-} + t_{0.02} \frac{S}{\sqrt{n} })<em />

(28.75-2.3824\frac{3.4}{\sqrt{64} },28.75 + 2.3824 \frac{3.4}{\sqrt{64} } )

(28.75 - 1.01252 , 28.75 + 1.01252)

(27.737 , 29.762)

<u><em>Final answer:-</em></u>

<em>98% confidence interval for the population mean mileage is </em>

(27.737 , 29.762)

<u><em /></u>

<em />

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