Explore BrainMass

Explore BrainMass

    Hypothesis test for a population mean

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Monitoring the ecological health of the Everglades-the bottom temperatures are recorded at the Garfield Bight station and the mean of 19.7 degrees C is obtained for 62 temperatures on 62 different days. Assuming sigma=1.6 degrees C, test claim that the pop mean is less than 20.0 degrees C. Use a 0.05 significance level to calculate test statistic.

    © BrainMass Inc. brainmass.com December 24, 2021, 5:07 pm ad1c9bdddf
    https://brainmass.com/statistics/hypothesis-testing/hypothesis-test-population-mean-29681

    SOLUTION This solution is FREE courtesy of BrainMass!

    Please see the attached Word document for solution.

    Monitoring the ecological health of the Everglades-the bottom temperatures are recorded @ the Garfield Bight station and the mean of 19.7 degrees C is obtained for 62 temperatures on 62 different days. Assuming o=1.6 degrees C, test claim that the pop mean is less than 20.0 degrees C. Use a 0.05 significance level to calculate test statistic.

    Solution:

    This is a one tailed test of hypothesis using the Z or standard normal distribution as the reference distribution for the test statistic since the sample size is large and we are assuming the population standard deviation, , is known.

    X is the random variable "temperature measurements". The sample size and sample mean are given in the problem, along with the population standard deviation.

    Given in the problem

    Null and alternative hypotheses

    Note that the alternative hypothesis is "less than" since this is what we are interested in discovering, if it is true. In general, what you want to know or discover goes in the alternative hypothesis. The null hypothesis almost always has "=" in it.

    Test statistic

    If the null hypothesis is true, this test statistic is a randomly selected member of a standard normal distribution.

    Rejection Region

    At the level of significance, the critical valueof the rejection region is the 5th percentile (corresponding to ) of the Z, or standard normal distribution. From the table, this value is -1.645. The rejection region is therefore:

    Test statistic < -1.645

    Conclusion

    Since the test statistic does not fall in the rejection region, at the 0.5 level of significance there is not enough evidence to reject the null hypothesis and conclude that the average temperature is less than 20.

    P-value

    Please note that an alternative to finding the rejection region, you could find the p-value and compare it to . If the p-value is less than , you can reject the null and conclude that the alternative is true. Otherwise there is insufficient evidence to reject the null. For this problem:

    The p-value is greater than , giving us the same conclusion as with the rejection region method.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:07 pm ad1c9bdddf>
    https://brainmass.com/statistics/hypothesis-testing/hypothesis-test-population-mean-29681

    Attachments

    ADVERTISEMENT