a county is considering raising the speed limit on the road because they claim t

Question

a county is considering raising the speed limit on the road because they claim that the mean speed of vehicles is greater than 45 miles per hour. A random sample of 25 vehicles has a mean speed of 49 miles per hour and a standard deviation of 5.1 miles per hour. At a=0.10, do you have enough evidence to support the county's claim?
a) calculate the standardized test.
t=
(round to 2 decimal places as needed)

b) decide whether to reject or fail to reject the null hypothesis. if the P-value is less than the level of significance, reject the null hypothesis. otherwise , fail to reject the null hypothesis

c) interprete the decision in the Context of the original claim . if the null hypothesis is rejected then there is sufficient evidence to support the county's claim that the mean speed of vehicles is greater than the posted speed limit. if the null hypothesis is rejected then there is not sufficient evidence to support the claim that the mean vehicle speed is greater than the posted speed limit.

Explanation / Answer

Claim: The mean speed of vehicles is greater than 45 miles per hour.

Hypotheses:

Null   H0:µ = µ0 = 45

Alternative   HA: µ > 45

Test Statistic:

t = (n)(Xbar - µ0)/s where

n = sample size = 25

Xbar = sample mean = 49

µ0   (given)     = 45

s = sample standard deviation = 5.1

So, tcal = 3.921

Distribution and Critical Value

Under H0, t ~ t with DF = n - 1   = 24

Given = .1

Critical Value, tcrit = upper

% point of tn-1 = 1.318

p-value of tcal = 0.000321

Decision Criterion (Rejection Region)

Reject H0 if |tcal| > tcrit or p-value <

Since |tcal| > tcrit, H0 is rejected.

Since p-value < , H0 is rejected.

Conclusion:

There is sufficient evidence to support the county's.

claim that the mean speed of vehicles is greater than

the posted speed limit

Claim: The mean speed of vehicles is greater than 45 miles per hour.

Hypotheses:

Null   H0:µ = µ0 = 45

Alternative   HA: µ > 45

Test Statistic:

t = (n)(Xbar - µ0)/s where

n = sample size = 25

Xbar = sample mean = 49

µ0   (given)     = 45

s = sample standard deviation = 5.1

So, tcal = 3.921

Distribution and Critical Value

Under H0, t ~ t with DF = n - 1   = 24

Given = .1

Critical Value, tcrit = upper

% point of tn-1 = 1.318

p-value of tcal = 0.000321

Decision Criterion (Rejection Region)

Reject H0 if |tcal| > tcrit or p-value <

Since |tcal| > tcrit, H0 is rejected.

Since p-value < , H0 is rejected.

Conclusion:

There is sufficient evidence to support the county's.

claim that the mean speed of vehicles is greater than

the posted speed limit

  

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