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The Statistical Abstract of the United States reported that the average cost per day of owning an automobile in the United states is $7.62. This includes the cost of the car, general maintenance, gasoline, and insurance. A researcher claims that college students' average daily ownership expenses are less than the national average. A random sample of 54 college students who own cars found the average cost per day to be $6.78 with standard deviation $1.77. Use a 5% level of significance to test the claim that a college student's average daily ownership expenses are less than the national average. State the Null and Alternate Hypotheses, calculate the test statistic, compute the P value for this test, state the alpha value, then state your conclusion. Is there enough evidence to support the claim?

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Answer:

Step-by-step explanation:

The null and the alternative can be computed as:

[tex]H_o : \mu = 7.62[/tex]

[tex]H_1 : \mu < 7.62[/tex]

[tex]Claim: \mu < 7.62[/tex]

[tex]\alpha= 0.05[/tex]

The critical value for a left-tailed test at [tex]\alpha= 0.05[/tex] = -1.645

The test statistics can be computed as:

[tex]Z = \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}} }[/tex]

[tex]Z = \dfrac{6.78 - 7.62}{\dfrac{1.77}{\sqrt{54}} }[/tex]

[tex]Z = -3.487[/tex]

The P-value = (Z< -3.487)

The P-value = 0.00024

Decision Rule: TO reject [tex]\mathbf{H_o}[/tex] at [tex]\alpha= 0.05[/tex], if test statistics is less than the critical value (left tailed)

Conclusion: We reject  [tex]\mathbf{H_o}[/tex] at ∝ = 5%, thus there is enough evidence to support the claim that the college students average daily ownership expenses are less than the national average.

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