Use the following situation to answer the next 2 questions: A manufacturer claims that a particular car will get at least 50 miles per gallon on the highway. The researchers of a consumer-oriented magazine believe this claim is too high and plan a test with a simple random sample of 30 cars. Assume the population standard deviation for individual cars is 2.3 miles per gallon. The researchers found the sample mean to be 49 miles per gallon, and they decided on using a = 0.05. (Hint: H n SD = H. Find the value of the test statistic. A.-2.38 B.-1.645 C.-0.43 D. 0.0087 E. 2.38 What is the conclusion of the hypothesis test? There evidence to reject the manufacturer's claim because sufficient:A. Is not; 49 miles per gallon is too close to the claimed 50 miles per gallon B. Is not; the p-value of 0.0087 is less than the significance level C. Is; the sample mean is less than the claimed mean D. Is; the p-value of 0.0087 is less than the significance level E. Is; the p-value of 0.0174 is less than the significance level

First question

The correct option is  A  

Second question

  The  correct option is  E

Step-by-step explanation:

From the question we are told that

    The  population  mean is  

     The  sample size is  n = 30  

      The population standard deviation is    

      The sample mean is  

        The  level of significance is  

The  null hypothesis is  

The  alternative  hypothesis is  

Generally the test statistics is mathematically represented as

=>    

=>    

Generally the degree of freedom is mathematically represented as

Generally from the student t distribution table the probability corresponding to  -2.38 to  the left  at a degree of freedom of is  

From the value obtained we see that

             hence  

The decision rule  

Reject  the null hypothesis  

The conclusion is  

There evidence to reject the manufacturer's claim because the p-value of  0.0174 is less than the significance level E

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w