Question

Records of 40 used passenger cars and 40 used pickup trucks were randomly selected to investigate the difference in how long the owners kept their vehicles. For cars, the mean was 5.3 years with standard deviation 2.2 years. For pickup trucks, the mean was 7.1 years with standard deviation 3.0 years. Find a 95% confidence interval for the true difference in means. Add a sentence. (Note that these are all sample results.)

Using the information in Problem One, test the claim that customers keep trucks no longer than cars. Assume that the standard deviations above were population standard deviations.

a. State the Null and the Alternative Hypotheses, explaining which is and which is .

b. Show the Test Statistics and the standardized test statistic

c. State the conclusion about the claim and how you made the decision.

Answer 1

The test hypothesis is

a)

b)

Now, the value of test static can be found out by following formula:

Since P-value of an upper tailed test is equal to \phi(|Z_0|)

P = 0.0011

c)

Since P = 0.00110 < 0.05, we reject the null hypothesis in favour of the alternative hypothesis\\

Since, the boundaries of the critical region are -Z_0.05 = -1.6448 and we note that Z0 falls in the critical region. Therefore, H0 is rejected

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