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    Population mean, one-tail test, p-value, standard deviation

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    This assignment has 9 questions to be answered. Some questions having multiple sub-questions. Please be sure to review the attachment.

    10.20 If the population standard deviation is known,
    but the sample size is less than 30, what assumption is
    necessary to use the z-statistic in carrying out a hypothesis
    test for the population mean?

    10.18 It has been claimed that no more than 5% of
    the units coming off an assembly line are defective.
    Formulate a null hypothesis and an alternative
    hypothesis for this situation. Will the test be one-tail
    or two-tail? Why? If the test is one-tail, will it be
    left-tail or right-tail? Why?

    10.28 For a sample of 12 items from a normally
    distributed population for which the standard deviation
    is   17.0, the sample mean is 230.8. At the 0.05 level
    of significance, test H0;greater than or equal to 220 versus H1 .
    Determine and interpret the p-value for the test.
    10.29 A quality-assurance inspector periodically

    10.44 The International Coffee Association has reported
    the mean daily coffee consumption for U.S. residents as
    1.65 cups. Assume that a sample of 38 people from a
    North Carolina city consumed a mean of 1.84 cups of
    coffee per day, with a standard deviation of 0.85 cups. In a
    two-tail test at the 0.05 level, could the residents of this
    city be said to be significantly different from their counterparts
    across the nation?

    10.74 It has been reported that 80% of taxpayers who
    are audited by the Internal Revenue Service end up
    paying more money in taxes. Assume that auditors are
    randomly assigned to cases, and that one of the ways
    the IRS oversees its auditors is to monitor the
    percentage of cases that result in the taxpayer paying
    more taxes. If a sample of 400 cases handled by an
    individual auditor has 77.0% of those she audited paying
    more taxes, is there reason to believe her overall
    "pay more" percentage might be some value other than
    80%? Use the 0.10 level of significance in reaching a
    conclusion. Determine and interpret the p-value for the
    test.

    11.70 According to the National Association of Homebuilders,
    the average life expectancies of a dishwasher
    and a garbage disposal are about the same: 10 years.
    Assume that their finding was based on a sample of
    n1 = 60 dishwashers and n2 = 40 garbage disposals, and
    that the corresponding sample standard deviations were
    s1 = 3.0 years and s2 = 3.7 years. Using the 0.02 level of
    significance, examine whether the population standard
    deviations for the lifetimes of these two types of
    appliances could be the same.

    Please be sure to review and answer the questions on the attachment.

    © BrainMass Inc. brainmass.com December 15, 2022, 8:09 pm ad1c9bdddf
    https://brainmass.com/business/managerial-statistics/business-statistics-population-mean-one-tail-test-p-value-standard-deviation-276299

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    10.20 If the population standard deviation is known, but the sample size is less than 30, what assumption is necessary to use the z-statistic in carrying out a hypothesis test for the population mean?

    The assumption needed is that the population distribution is normal or approximately normal.

    10.18 It has been claimed that no more than 5% of the units coming off an assembly line are defective. Formulate a null hypothesis and an alternative hypothesis for this situation. Will the test be one-tail or two-tail? Why? If the test is one-tail, will it be left-tail or right-tail? Why?

    H0: The proportion of units coming out of the assembly >= 0.05
    H1: The proportion of units coming out of the assembly < 0.05
    Please note that whatever we claim should be written as an alternate hypothesis.
    This is a one tail test, as we want to establish that the production system is in good shape and does not produce more than 5% defective items. However, if it produces significantly less than 5% we are not bothered.

    10.28 For a sample of 12 items from a normally
    distributed population for which the standard deviation
    is 17.0, the sample mean is 230.8. At the 0.05 level
    of significance, test H0;greater than or equal to 220 versus H1 .
    Determine and interpret the p-value for the test.

    Sample Mean 230.8
    Population Standard Deviation 17
    Sample size 12
    Standard Error 4.91
    This is a one tail test as we are testing whether the sample mean is less than 220 or not. It is a z-test as although the sample size is less than 30, we know the standard deviation and the population distribution is normal.
    Level of significance 0.05
    Z-observed 2.200723379
    Z-critical 1.645
    Since z-critical is less than z-observed, we reject the null hypothesis and conclude that mean is statistically significantly greater than 220.
    p-value 0.0139
    The p-value of 0.0139 indicates that if the significance level is 0.0139 or above, we will reject the null hypothesis and conclude that the mean is statistically higher than 220.

    10.44 The International Coffee ...

    Solution Summary

    Population mean, one-tail test, p-value and standard deviation is examined.

    $2.49

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