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Chapter 9: Q. 77 (page 543)

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on

average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of

49students and obtain a sample mean of 5.1with a sample standard deviation of 1.2Do the data support your claim at the

1%level?

Short Answer

Expert verified

The claim is supported at the 1% level .

Step by step solution

01

Given Information

For H0, mean is =4.5

For Ha, mean is鈮�4.5

localid="1650205190437" 伪=0.01

Testt=0.995

Df=49

02

Explanation

Using the formula below:

t=(X炉-渭)sn

Critical Value = 2.6822

Reject H0 for|t|>2.6822

t=4.5-5.11.249=-4.21.2=-3.5

Reject H0 , p - value =0.001

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Most popular questions from this chapter

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the TypeIerror is:

a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than , when in fact, it is not higher

Driver error can be listed as the cause of approximately 54% of all fatal auto accidents, according to the American Automobile Association. Thirty randomly selected fatal accidents are examined, and it is determined that 14 were caused by driver error. Using 伪 = 0.05, is the AAA proportion accurate?

A particular brand of tires claims that its deluxe tire averages at least 50,000miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28tires surveyed, the mean lifespan was 46,500miles with a standard deviation of 9,800miles. Using alpha =0.05, is the data highly inconsistent with the claim?

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5a percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?

localid="1650439913140" a.H0__________

b.Ha __________

You are performing a hypothesis test of a single population mean using a Student鈥檚 t-distribution. What must you assume about the distribution of the data?
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