Consider the following information to validate the hypothesis that the mean of the population
is at most 30 at 5% level of significance.
Sample size = 45, mean of the sample = 38, variance = 4
What will be conclusion if the level of significance is taken as 1%? Mention the observations, if
any.
1. The following null and alternative hypotheses need to be tested:
This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.
Based on the information provided, the significance level is
degrees of freedom, and the critical value for a right-tailed test is
The rejection region for this right-tailed test is
The t-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value for right-tailed is and since it is concluded that the null hypothesis is rejected.
Therefore, there is not enough evidence to claim that the population mean
is at most 30, at the significance level.
2. The following null and alternative hypotheses need to be tested:
This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.
Based on the information provided, the significance level is
degrees of freedom, and the critical value for a right-tailed test is
The rejection region for this right-tailed test is
The t-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value for right-tailed is and since it is concluded that the null hypothesis is rejected.
Therefore, there is not enough evidence to claim that the population mean
is at most 30, at the significance level.
Therefore there is not enough evidence to claim that the population mean
is at most 30, at significance level and at significance level.
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