Exam 3 study guide - GBS 221 Review for Exam 3 1 The Colonial Canning Company of Claremont California uses a machine to fill its 18-ounce cans of

Exam 3 study guide - GBS 221 Review for Exam 3 1 The...

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GBS 221 Review for Exam 3 1. The Colonial Canning Company of Claremont, California uses a machine to fill its 18-ounce cans of kumquats. If the machine performs improperly, it is readjusted. A sample of 50 cans is found to have a mean of 18.9 ounces. The population is known to have a standard deviation of 4.7 ounces. Test at the 95% confidence level. a. Perform a hypothesis test to determine if the machine should be readjusted. Show all steps for full credit. Ho: μ = 18 Ha: μ ≠ 18 Z= 1.96 * ((18.9 – 18) / (4.7 / √50)) Z= 1.354 =.9115 .9115 < .95 Do not reject, do not readjust n σ/ μ x z 0 b. If the sample was 500 cans, yielding the same mean, should the machine be readjusted? Z = 1.96 * ((18.9 – 18) / (4.7 / √500) Z = 4.28 4.28 > 1.96 Reject, Readjust the machine
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2. A student believes that no more than 20% of the students who finish a statistics course get an A. A random sample of 100 students was taken. Twenty-four percent of the students in the sample received A’s. a. State the null and alternative hypotheses. n=100 Ho : P ≤ .24 Ha: P > .24 b. Using a critical value, test the hypothesis at the 1% level of significance. Z= .24 - .2 / √((.2(1-.2) / 100)) Z= 1 Do not reject Ho, 1 < 2.33, there is not sufficient evidence at a=1% to conclude that more than 20% of the students get an A. c. Using a p -value, test the hypothesis at the 1% level of significance. Critical value of Z=1 =.8413 since Left tail test 1 - .8413 = 0.1587 (same conclusion as part b) 3. The following sample information is given concerning the ACT scores of high school seniors form two local schools. School A School B
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1 n = 14 2 n = 15 1 x = 25 2 x = 23 2 1 = 16 2 2 = 10 Develop a 95% confidence interval estimate for the difference between the two populations. n σ + n σ = σ 2 2 2 1 2 1 X 2 X 1 Since the standard deviation is already squared making it variance there is no need to square in function 25 – 23 ± 1.96 * √((16/14) + (10/15)) 2 ± 2.6366 -0.637 to 4.637 the results prove two tail test by one interval being negative and one interval being positive.
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4. A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five ago. Results are summarized below. Use a hypothesis test to test if the proportion has increased significantly? Let = 0.05. Sample Size Number Considered Themselves Overweight Current Sample (c) 300 150 Previous Sample (p) 275 121 Question asks for the proportion, a big hint showing this is going to be a proportion hypothesis test. Asking increased significantly means Ho: Pc – Pp ≤ 0 Ha: Pc – Pp > 0 Use calculator for this problem Steps: Stat Test 2-propZtest Z=1.44 P-Value=.0749 .05 < .0749 Do not reject Ho
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5. To catch more criminals, the governor has budgeted more money to put more police on our city streets. The decision was based on the following data: # of Police: 13 15 23 25 15 10 9 20 # Arrests: 8 9 12 18 8 6 5 10 a.
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