Paint used to paint lines on roads must reflect enough light to be clearly visib

Question

Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let denote the true average reflectometer reading for a new type of paint under consideration. A test of H0: = 20 versus Ha: > 20 based on a sample of 14 observations gave t = 2.9. What conclusion is appropriate at each of the following significance levels?

(a) = .05

Reject H0 Fail to reject H0    

(b) = .01

Reject H0 Fail to reject H0    

(c) = .001

Reject H0 Fail to reject H0    

e % Chapter 10 webassign.net/wetauderu Assignment-Respor m NSA cllected necords of personal telephone calls they had made ra. may need tune the appuonate table Aeeend. Atoamner tho "nsta Questio Paint used to sart lin es on roads must .ofoot enou 1ght to be dearly vubl.. ·Let denote the tive average reflectsnete reading nor a netype of paint und consideration. Atea ofiV .29eersus M.>20bned on a 2.3.What condlusion is appropriate at each of the following significance levels? o 14 observations gave t the pant use O Fal to reject H Expert A te) a-01 Fad to relect writing Ifetine and a narmal probability Deg Since

Explanation / Answer

Null and alternative hypothesis is

H0: = 20 versus Ha: > 20

Our hypothesis is one tail test because the alternative hypothesis has greater than sign.

Sample size = n = 14

Degrees of freedom = n - 1 = 14 - 1 = 13

Test statistic = t = 2.9

a) = .05

Critical value = 1.771 ( Using t table)

Test statistic > critical value we reject null hypothesis( H0).

b) = .01

Critical value = 2.650 ( Using t table)

Test statistic > critical value we reject null hypothesis (H0).

c) = .001

Critical value = 3.852 ( Using t table)

Test statistic < critical value we fail to reject null hypothesis (H0).

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