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# Hypothesis Testing of Mean: P-value Method

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Use the p value method to determine whether or not to accept or reject the null and alternate hypotheses.

1. You are determining whether the true mean is less than 11 with a 95% confidence based on the following statistics:

n(sample size) = 14 sample mean = 9 sample st. dev = 4

2. You are trying to determine whether the true mean is not equal to 10, with a 95% confidence based on the following descriptive statistics.

n = 14 sample mean = 12 sample st. dev = 3

3. You are trying to determine whether the true mean is greater than 1 with a 96% confidence based on the following descriptive statistic:

n = 16 sample mean = 3 population st. dev = 4

https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-mean-value-method-394610

#### Solution Preview

Null and alternate hypotheses
Use the p value method to determine whether or not to accept or reject the null and alternate hypotheses.

1. You are determining whether the true mean is less than 11 with a 95% confidence based on the following statistics:

n(sample size) = 14 sample mean = 9 sample st. dev = 4
The null hypothesis tested is
H0: Population mean ≥ 11 (µ ≥ 11)
The alternative hypothesis is
H1: Population mean < 11 (µ < 11)
Significance level = 0.05
Test Statistic used is . Given that = 9, n = 14, s = 4,  = 11
Therefore, = -1.870828693
Decision rule: Reject the null hypothesis, if the p-value is less than the significance level 0.05.
P-value = P (t13 < -1.870828693) = 0.042022978
Conclusion: Reject the null hypothesis, since the p-value is less than the significance level 0.05. The sample provides enough evidence to conclude that the true mean ...

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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