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(a)
To find:
The null and alternative hypotheses.
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Answer to Problem 18E
Solution:
The null hypothesis is
Explanation of Solution
Given information:
Joe wants to get the best possible price on a used luxury car. He lives near the border of two states, and he believes that prices are better across the state line, i.e., the mean selling price for used luxury cars is lower in the other state.
The null hypothesis is a statement of no difference, that there is no significant difference between the two phenomena. It is considered to be true until it is nullified by statistical evidence for an alternative hypothesis.
An alternative hypothesis is a contradicting statement to the null hypothesis and states a significant difference between the two phenomena It is accepted when the null hypothesis is false.
Calculation:
From the given information:
Let
Therefore the null hypothesis is
(b)
To find:
Which distribution to be used for test statistic, and the level of significance.
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Answer to Problem 18E
Solution:
The distribution used is standard normal variate (one-tailed z test), and the level of significance is 5% or 0.05.
Explanation of Solution
Since both the sample sizes are greater than 30,
According to the null hypothesis, one-tailed test is to be applied.
From the given information, the level of significance is 5% or 0.05.
(c)
To find:
The test statistic
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Answer to Problem 18E
Solution: The test statistic is 2.05
Explanation of Solution
Given information:
For Joe’s state:
The
For the other state:
The sample size is 40, the mean selling price is
Test statistics is a random variable which is calculated from the sample data and used in hypothesis testing.
Test statistic calculates the degrees of acceptance between sample data and null hypothesis.
Formula used:
The test statistic for a hypothesis test for two population means is:
Where:
and
Calculation:
The test statistic for a given hypothesis is,
Substitute
It is given that the null hypothesis for the given proportion is
Thus, the test statistic is
(d)
To find:
The conclusion by comparing the
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Answer to Problem 18E
Solution:
The null hypothesis is and it shows the selling prices of used luxury cars are better in the other state.
Yes, there is sufficient evidence to show that the mean selling prices of used luxury cars are lower in the other state.
Explanation of Solution
Formula used:
The
Calculation:
This is a right-tailed test, so p-value = P
Conclusion:
Test statistic is
Since the
This shows the selling prices of used luxury cars are better in the other state.
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Chapter 11 Solutions
Beginning Statistics, 2nd Edition
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