220 ‐ Quiz 3 – 10 Points Chapters 9 Name: ………………………………………………. ID: ……………… Exam Rules: • Turn off your cell phone. • You cannot share calculators. • Got problems? Raise your hand. • The exam consists of two parts: - Conceptual (5 Points) - Calculation (5 Points) • You should have 6 pages (including tables). Count them. It is your responsibility to ensure that you have a complete exam • Relax, you may think better. ____________________ Good Luck ☺ Answers for problem # 1 1 2 3 4 5 A
C
D
C
C
Problem # 1 Select the best answer and write it in the appropriate space in the table on the first page (1 point each) 1. In a test of hypothesis, the null hypothesis is that the population mean is equal to 125 and the alternative hypothesis is that the population mean is greater than 125. A sample of 100 elements selected from this population produced a mean of 129.9 and a standard deviation of 17. What is the approximate p‐value for this test? a. .0020 b. .0200 c. .0040 d. .0080 2. In a left‐tailed test of hypothesis, the sign in the alternative hypothesis is: a. not equal to (≠) b. greater than (>) c. less than (<) d. less than or equal to (≤) 3. When carrying out a large sample test of H0: μ = 10 vs. Ha: μ > 10 by using a rejection point, we reject H0 at level of significance α when the calculated test statistic is: a. Less than zα
b. Less than ‐zα
c. Greater than zα/2
d. Greater than zα
4. For a one‐tailed test, the probability value (p‐value) is: a. the area under the curve between the mean and the observed value of the sample statistic b. twice the area under the curve between the mean and the observed value of the sample statistic c. the area in the tail beyond the observed value of the sample statistic d. twice the area in the tail beyond the observed value of the sample statistic 5. The following four steps must be taken to perform a test of hypothesis using the p‐value approach: 2
1. 2. 3. 4. Calculate the p‐value. Select the distribution to use. Make a decision. State the null and alternative hypothesis. The correct order for performing these steps is: a. 4, 1, 2, 3 b. 2, 3, 1, 4 c. 4, 2, 1, 3 d. 3, 2, 1, 4 Problem # 2 The CEO of XYZ‐Mart, a department store chain, asks his director of marketing in a board meeting how much each customer spends in XYZ‐Mart stores each year. Not having investigated this question before, the director estimates that each customer spends about $300 per year. In order to check the validity of this estimate, he conducts a survey of 100 customers who have shopped at XYZ‐Mart stores. These customers spent an average of $304.66 in the past year with a standard deviation of $17.45. a. State the null and alternative hypotheses. (1 point) Ho: μ = 300
H1: μ ≠ 300
b. Calculate the test statistic or the p‐value for this test. Test statistic: Z o =
(1 point) 304.66 − 300 4.66
=
= 2.6705.
17.45 / 100 1.745
The p-value is p = 2 × (.5000 – .4962) = .0076
c. Can the director reject his estimate at the 5% level of significance? (1 point) Since Zc = 1.96 < Zo = 2.67, hence we we reject the accountant’s estimate at the
5% level of significance.
The p-value is easily less than .05. Therefore, we reject the accountant’s estimate
at the 5% level of significance.
3
Problem # 3 Complete the following contingency table that illustrates the possible outcomes of a statistical hypothesis test. (2 points) Actual Situation Ho Is true Ho Is false Do not reject Ho Correct decision
Type II
β
Reject Ho Type I
α
Correct decision
Decision 4