Answer to Question #285497 in Statistics and Probability for Jay

Question

A test on car braking reaction times for mean between 18 and 30 years old have produced a mean

and standard deviation of 0.610 sec. and 0.123 sec, respectively. When 40 male drivers of this age

group were randomly selected and tested for their breaking reaction times, a mean of 0.587

second came out. At the α = 0.10 level of significance, test the claim of the driving instructor that

his graduates had faster reaction times.

Solution:

I. Statement of the Hypothesis:

Ho :

H1 :

II. Statistical Test:

III. Level of Significance and Critical Value:

IV. Computed value of Z:

V. Conclusion:

Answer 1

$\bar x$ =0.610

$\sigma$ =0.123

$\mu$ =0.587

n=40

(a).the test hypothesis

H_{o :}$\mu$ $\le$ 0.587

Ha:$\mu$ >0.587

(b).Statistical test

z-test

(c).Level of significance is 10% and the critical value is1.645

(d).computed value of z

$z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt n}}$

$z=\frac{0.610-0.587}{\frac{0.123}{\sqrt 40}}$

$z=1.18264$

(e).conclusion

since the computed z value,1.18264 is less than the critical value 1.645 ,we fail to reject the null hypothesis.