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natima [27]
3 years ago
6

It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 122 feet. A transportat

ion researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 38 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 116 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the appropriate table: z table or t table) a. State the null and the alternative hypotheses for the test.

Mathematics
1 answer:
madreJ [45]3 years ago
4 0

Complete Question

The complete question is shown on the first uploaded image

Answer:

the null hypothesis is  H_o  :  \mu =  122

the alternative hypothesis is H_a  :  \mu \ne  122

The test statistics is  t =  - 1.761

The p-value is  p =  P(Z  <  t ) = 0.039119

so

    p  \ge 0.01

Step-by-step explanation:

From the question we are told that

   The population mean is  \mu  = 122

     The sample size is  n=  38

    The sample mean is  \= x  =  116 \ feet

     The standard deviation is \sigma  =  21

     

Generally the null hypothesis is  H_o  :  \mu =  122

                the alternative hypothesis is H_a  :  \mu \ne  122

Generally the test statistics is mathematically evaluated as

         t =  \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }

substituting values

         t =  \frac { 116 -  122 }{\frac{ 21 }{ \sqrt{ 38} } }

         t =  - 1.761

The p-value is mathematically represented as

      p =  P(Z  <  t )

From the z- table  

     p =  P(Z  <  t ) = 0.039119

So  

     p  \ge 0.01

 

         

     

           

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