Question

26. In a random sample of 95 college students, 40 wished they would have chosen a different major. Use the following steps to construct a 95% confidence interval for the true proportion of all students who wished they would have chosen a different major. a. Find the number of sample values, n b. Find the sample proportion, B c. Find the critical z-score, 2/2 d. When calculated correctly, E = 0.0993. Construct a confidence interval for the population proportion, p. e. Write a sentence summarizing the confidence interval 27. A random sample of 175 people in a city results in 52% who would vote for Proposal T. The mayor claims that the actual percentage of voters is more than 55%. Use the following steps to test the claim at a 0.05 significance level. a. State the claim b. State the opposite of the claim c. State the null hypothesis d. State the alternative hypothesis e. State the type of test (left tailed, right tailed, or two tailed). Find the critical value and make a sketch. f. Identify p. p, q,and n. When calculated correctly, Zsample=-0.80 g. Is your verdict "reject Ho" or "fail to reject H."? h. Using the flow chart to guide you, write a conclusion

Answer 1

n = 95 こ C. we 2012 P-Zain 26.a College students. b. 8 = Number of students chosen different measure yo Total number of students 95 I È = 0.4211 At d = 0.05, by using standard Normal table obtain 20.025 = 1.96 d. Since E = Zail 6(1-01 Ŕ -P 2-test for ~ Nlail) proportion PCI-bl This (critical value) (standard Espor) to (1.b) n = (1-96 1 (0-0507) = 0·0993 Now by using Equation Swecon write b-P al C 2012 I-a Ê (1-6) h because Nicol) (2- n E = Zan < an) n ar or PL-E b-PSE) = 1-2 P(Å-E E P S E +5) = 1-2 p(0.4211 - 0.0993 SP 50.4211 +0-0993) - 0.95 or ar P(0.3218 Ses 0.5204) = 0.95

So are 95 ". Confidence Interval= (0.3218, 0.5204) We 95 of Confident that the tone population proportion will belong to interval (0.3218, 0.5204) We 27.0 Here subbose P denotes the population proportion and k denotes the sample proportion. have claim that actual percentage of voters is more than 55%.(P >0.55) 6 The opposite of claim us that the actual percentage of voters is less than or equal to 55%. (P<0.55) © By considering post a and b' and have the will hy bothesis is Ho: P<0.55 Us Ha: Pro we The opposite of Noll es alternative Thus Alternative is given by Ha! p > 0.55 thus our test 2 Since Mo: P>0.55 is right tailed test.

Za the critical value By table 20.05 = 1.65 6 = 0.52 , n=175, under null hy botheso b = 0.55 q=1-p=0=45 Since (9 Р 2 = N N (oll) pq n T 2 = 0.52 – 0.55 0.80 (0:55) 00:45) 175 with critical value since thus we com not reject the g. By compairing 2 < 20.05 Null hypothesis. Zeritian 162015212=-0.80 = 165 Do not reject Null hy bothesis