Please show all work so I can use as a guideline Thanks for

Please show all work so I can use as a guideline, Thanks for your help

The speed limit on Interstate 80 gets as high as 75 mph, especially in rural areas. To monitor the speed of cars, a local police station sets up a radar gun along a stretch of the highway that has a posted speed limit of 75 mph. The police station wants to know if they should propose that the speed limit be decreased to 70 mph. If the sample mean speed of cars is significantly greater than 75 mph, this would provide evidence to support their hypothesis that the average speed of cars is greater than 75 mph (and thus, the posted speed limit should be lowered). The radar gun detects 350 cars and the average speed is 77 mph with a standard deviation of 15. For this part, write down the two hypotheses and find the test statistic for the hypothesis test. You must show all work.

Solution

Set Up Hypothesis
Null Hypothesis H0: U<75
Alternate Hypothesis H1: U>75
Test Statistic
Population Mean(U)=75
Sample X(Mean)=77
Standard Deviation(S.D)=15
Number (n)=350
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =77-75/(15/Sqrt(349))
to =2.494
| to | =2.494
Critical Value
The Value of |t ?| with n-1 = 349 d.f is 1.649
We got |to| =2.494 & | t ? | =1.649
Make Decision
Hence Value of | to | > | t ?| and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 2.4944 ) = 0.00654
Hence Value of P0.05 > 0.00654,Here we Reject Ho