The observations in the sample are random and independent. The underlying population distribution is approximately normal. We consider H_{0}: =15 against H_{a}: 15. with =0.05.
Sample statistics: = 16, s_{x}= 0.75, n= 10.
1. For the given data, find the test statistic
t-test=4.22 |
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t-test=0.42 |
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t-test=0.75 |
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z-test=8.44 |
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z-test=7.5 |
2.
Decide whether the test statistic is in the rejection region and whether you should reject or fail to reject the null hypothesis.
the test statistic is in the rejection region, reject the null hypothesis |
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the test statistic is outside of the rejection region, reject the null hypothesis |
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the test statistic is in the rejection region, fail to reject the null hypothesis |
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the test statistic is outside of the rejection region, fail to reject the null hypothesis |
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more data is needed to decide |
Solution:
This is a two tailed test.
The test statistics,
t =( - )/ (s /n)
= ( 16 - 15 ) / ( 0.75 / 10 )
= 4.22
Critical value of the significance level is α = 0.05, and the critical value for a two-tailed test is
= 2.262
Since it is observed that t = 4.22 > = 2.262, it is then concluded that the null hypothesis is rejected.
The test statistic is outside of the rejection region, reject the null hypothesis.
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