The paint used to make lines on roads must reflect enough light to be clearly vi

Question

The paint used to make 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 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.) (a) n = 16, t = 3.1, ? = 0.05 P-value = State the conclusion in the problem context. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. (b) n = 9, t = 1.8, ? = 0.01 P-value = State the conclusion in the problem context. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. (c) n = 28, t = ?0.7 P-value = State the conclusion in the problem context. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Explanation / Answer

a.

H0: ? = 20 versus Ha: ? > 20

critical value

the value of |t ?| with n-1 = 15 is +1.7531

we got |to| =3.1 & | t ? | =1.7531

make decision

hence value of |to | > | t ? | and here we reject Ho

p-value :two tailed ( double the one tail ) - Ha : ( p > 3.1 ) = 0.003659

hence value of p0.05 > 0.003659 ,here we reject Ho

reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20

b.

H0: ? = 20 versus Ha: ? > 20

critical value

the value of |t ?| with n-1 = 8 is +2.8965

we got |to| =1.8 & | t ? | =2.8965

make decision

hence value of |to | < | t ? | and here we do n't reject Ho

p-value :two tailed ( double the one tail ) - Ha : ( p > 1.8) = 0.054777

hence value of p0.01 < 0.054777 ,here we don't reject Ho

do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20

c.

Critical Value

The Value of t ? at 0.05 LOS with n-1 = 27 is +1.7033

P-Value : Right Tail - Ha :( P > -0.7) = 0.755042

H0: ? = 20 versus Ha: ? > 20

critical value

the value of |t ?| with n-1 = 27 is +1.7033

we got |to| =-0.7 & | t ? | =1.7033

make decision

hence value of |to | < | t ? | and here we do n't reject Ho

p-value :two tailed ( double the one tail ) - Ha : ( p > -0.7) = 0.755042

hence value of p0.05 < 0.755042 ,here we don't reject Ho

do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20

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