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# Statistics Problem Set: Rejecting the Null Hypothesis

3. Consider the hypothesis test given by
H_0: u = 670
H_1: u does not equal 670
In a random sample of 70 subjects, the sample mean is found to be 678.2. The population standard deviation is known to be omega = 27.
(a) Determine the P-value for this test. (Show work)
(b) Is there sufficient evidence to justify the rejection of H_0 at the omega = 0.02 level? Explain.

4. The playing times of songs are normally distributed. Listed below are the playing times (in seconds) of 10 songs from a random sample. Use a 0.05 significance level to test the claim that the songs are from a population with a standard deviation less than 1 minute.

448 231 246 246 227 213 239 258 255 257

(a) What are your null hypothesis and alternative hypothesis?
(b) What is the test statistic? (Show work)
(c) What is your conclusion? Why? (Show work)

5. Given a sample size of 25, with sample mean 736.2 and sample standard deviation 82.3, we perform the following hypothesis test
H_0: u = 750
H_1: u < 750
What is the conclusion of the test at the omega = 0.10 level? Explain your answer. (Show work)

#### Solution Preview

3. Consider the hypothesis test given by
H_0: u = 670
H_1: u does not equal 670
In a random sample of 70 subjects, the sample mean is found to be 678.2. The population standard deviation is known to be omega = 27.
(a) Determine the P-value for this test. (Show work)

Test value t=(678.2-670)/(27/sqrt(70))=2.54
P value=TINV(2.54,69,2)=0.0133 (TINV is a function in EXCEL, 69 is the degree of freedom, 2 means two tailed t test).

(b) Is there sufficient evidence to justify the rejection of H_0 at the omega = 0.02 level? Explain.

Since P value ...

#### Solution Summary

The expert rejects the null hypothesis in statistics.

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