Question

A county is considering rasing the speed limit on a road because they claim that the mean speed of vehicles is greater than 40 miles per hour. A random sample of 20 vehicles has a mean speed of 42 miles per hour and a standard deviation of 4.3 miles per hour. At α=0.05​, do you have enough evidence to support the​ county's claim? Complete parts​ (a) through​ (d) below.​(a)

Write the claim mathematically and identify

Upper H 0H0

and

Upper H Subscript aHa.

Choose the correct answer below.

A.

Upper H 0H0​:

muμless than or equals≤4040

Upper H Subscript aHa​:

muμgreater than>4040

B.

Upper H 0H0​:

muμnot equals≠4040

Upper H Subscript aHa​:

muμequals=4040

C.

Upper H 0H0​:

muμgreater than or equals≥4040

Upper H Subscript aHa​:

muμless than<4040

D.

Upper H 0H0​:

muμequals=4040

Upper H Subscript aHa​:

muμnot equals≠4040

​(b) Calculate the standardized test statistic.

t=

​(Round to two decimal places as​ needed.)

Use technology to calculate the​ P-value.

​P-value=

​(Round to three decimal places as​ needed.)

​(c) Decide whether to reject or fail to reject the null hypothesis.

​(d) Interpret the decision in the context of the original claim.

Answer 1

Heru, we have nuu 42 543

2.08 0.0256 :lo. 026) Roundんthru, deci mal pla ua Pen hown
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