Sample Hypotheses Formulation(1)

Sample Hypotheses Formulation(1) - SampleFormulas problems....

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Sample Formulas The following problems provide insight into how we use  hypothesis testing to make determinations about business  problems.  The statistical procedures outlined are standard  tests. The examples were performed using an Excel add-on.    Problem 1.   The manager of a paint supply store wants to determine whether the  amount of paint contained in 1-gallon cans purchased from a nationally known  manufacturer actually averages 1gallon. It is known from the manufacturer's  specifications that the standard deviation of the amount of paint is equal to .02 gallon. A  random sample of 50 cans is selected, and the mean of the amount of paint per 1-gallon  can is found to be .995 gallon . a. State the null (N) and the hypotheses (H).     ANSWER:   H 0: :  µ  = 1 H 1 :    µ    1 b. Is there evidence that the mean amount is different from 1.0 gallon (use alpha       α    .01).     ANSWER:There is insufficient evidence to reject the null hypothesis as the Z test  statistic  falls within the region of non-rejection Intermediate Calculations Standard Error of the Mean 0.002828427 Z Test Statistic - 1.767766953 Two-Tailed Test Lower Critical Value - 2.575831338 Upper Critical Value 2.575831338 p -Value 0.077099777 Do not reject the null hypothesis Interpret the meaning of the p-value.
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ANSWER: the p-Value is greater than the level of significance.  Therefore,the  probability is highly unlikely that more sample values will fall outside the region of non- rejection. Problem 2.    ATMs must be stocked with enough cash to satisfy customers making  withdrawals over an entire weekend. But if too much cash is unnecessarily kept in the  ATMs, the bank is forgoing the opportunity of investing the money and earning  interest. Suppose that at the particular branch the expected (i.e., population) mean  amount of money withdrawn from ATMs per customer transaction over the weekend is  $160, with an expected (i.e., population) standard deviation of $30. a. State the null (N) and the hypotheses (H).     ANSWER:       H 0: :  µ  = $160 H 1 :    µ    $160 b. If a random       sample of 36   customer   transactions is   examined and   the sample   mean   withdrawal is $172, is there evidence to believe that the population average   withdrawal is no longer $160? (Use a .05 significance level). ANSWER: Intermediate Calculations Standard Error of the Mean 5 Z Test Statistic 2.4 Two-Tailed Test Lower Critical Value -1.959962787 Upper Critical Value 1.959962787 p -Value 0.016395058 Reject the null hypothesis
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The Z Test Statistic falls outside the region of non-rejection.  Therefore, we should reject  the null hypothesis.   c. Interpret the meaning of       the p-value.
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