Question

132 /texttornework 2001) Draw the Distribution and mark off your ample means. Conspite the Test Statistic: Calculate the p value • Do you Reject the H or Fail to Reject the H.? • Write out a statement describing your conclustion. 2.2 Confidence Interval High school students who take the SAT mathematics exam a second time generally score higher than on their first attempt. The change in score has a Normal distribution with a standard deviation y = 50. A random sample of 1000 students gain an average of 1 22 points on their second try 1. Compute a 95% confidence interval for the mean score gain in the population of all students who take the test a second time. 2. Will the confidence interval become larger or smaller if we descrease the level of confidence to say 90%? 3. Will the confidence interval become larger or smaller if we increase our sample size. Why? 4. How large of a sample of high school students in the above example would be needed to estimate the mean change p in SAT scores to be within 1.5 points with 95%.

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Answer 1

2.2) 50 n = 1000 a) I = 22 95% confidence interval for population - 22/2 o su s x + 2212 - 2 1x 22 – 1.96x 50 < " C 22 + 1.96 x 50 I coo Jooo s u 22 - 3. 1 18.9 22 + 3.1 < 25.1 s b) to 90%. Zal for go% confidence interval - 1.645 The confidence interval become smaller if we decrease the level of confidence, because the margin of error will decrease. The confidence increase the of error will interval become smaller if we sample size because the margin decrease N 4268.4 /1.96*50 = (-36x50) = 4268.4 n = 1.5