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
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
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.
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
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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