An automobile manufacturer claims that its jeep has a 36.1 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 150 jeeps, they found a mean MPG of 35.8. Assume the standard deviation is known to be 2.4. A level of significance of 0.02 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision.

Since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is different from 36.1 MPG (the claim by the manufacturer)

Step-by-step explanation:

Information given  

represent the sample mean for the MPG

represent the population deviation

sample size  

represent the value to check

represent the significance level for the hypothesis test.  

t would represent the statistic

represent the p value

System of hypothesis

We need to conduct a hypothesis in order to check if manufacturer is incorrect, the null and alternative hypothesis are:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

 (1)  

Replacing we got:

P value

Since we are conducting a bilateral test we can find the p value like this:

Conclusion

Since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is different from 36.1 MPG (the claim by the manufacturer)

d. vertex

step-by-step explanation:

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500