Discover how IDNLearn.com can help you find the answers you need quickly and easily. Our experts provide timely and precise responses to help you understand and solve any issue you face.

To compare the dry braking distances from 30 to 0 miles per hour for two makes of​ automobiles, a safety engineer conducts braking tests for 35models of Make A and 35 models of Make B. The mean braking distance for Make A is 41feet. Assume the population standard deviation is 4.6 feet.The mean braking distance for Make B is 45feet. Assume the population standard deviation is 4.3 feet.At alphaequals0.10​,can the engineer support the claim that the mean braking distances are different for the two makes of​ automobiles

Sagot :

Answer:

There is sufficient evidence to support the claim.

Step-by-step explanation:

Given

[tex]\alpha = 0.10[/tex]

Make A

[tex]\bar x_1 = 41[/tex]

[tex]\sigma_1= 4.6[/tex]

[tex]n = 35[/tex]

Make B

[tex]\bar x_2 = 45[/tex]

[tex]\sigma_2 = 4.3[/tex]

[tex]n = 35[/tex]

First, we state the null and alternate hypothesis

[tex]H_0 : \mu_1 = \mu_2[/tex]

[tex]H_1 : \mu_1 \ne \mu_2[/tex]

Next, calculate test statistic:

[tex]z = \frac{(\bar x_1 - \bar x_2)-(\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}[/tex]

[tex]z = \frac{(41- 45)-0}{\sqrt{\frac{4.6^2}{35}+\frac{4.3^2}{35}}}[/tex]

[tex]z = \frac{-4}{\sqrt{0.6046+0.5283}}[/tex]

[tex]z = \frac{-4}{\sqrt{1.1329}}[/tex]

[tex]z = \frac{-4}{1.0643}[/tex]

[tex]z = -3.7583[/tex]

The critical value at [tex]\alpha = 0.10[/tex] is: [tex]\±1.282[/tex]

[tex]-3.7583 < -1.282[/tex]

So, we reject [tex]H_0[/tex]

This implies that; there is sufficient evidence to support the claim.