Question

At a local high school, the juniors and seniors compete to see who has a better average on a statistics test. Ten randomly selected junior had an average of 38.0 points with a standard deviation of 2.9 and 14 randomly selected seniors had an average of 31.2 points with a standard deviation of 6.2. Assume both populations follow a normal distribution We want to perform a test to see if on average juniors perform better on the test. a. Define the parameters and state the hypotheses. [3pts] b. Find the observed sample statistic and the test statistic. Use proper notation for the sample statistic (or ), and clearly identify your test statistic as either a z-score or a t-score. [4pts] c. Find the p-value of your test statistic. You are required to graph the test statistic on its corresponding distribution, shade the appropriate area, and provide correct calculator documentation. Box final answer. [3pts] d. Make a generic decision about H, [2pts] e. Make a conclusion in the context of the problem. [2pts]

Answer 1

Answer:-

a lunios (6 let en population mean of junin the = population mean of seniors So We test the null of alternative Hypothesis of this parameted, Hoi u = 12 vis Hii 117 42 Celain) test Statistie Here use sample statisti? statisti? ě and + because population roejances que unknown. test_statistic to XI - X2 for unequal variances use scose 2 Sp²+ ni h2 72 * Sample 10 of junios where le mean of X = sample mean of junior Senios X = 38 njia X2 = 31.2 h2=14 Size Sample 37 andard deviation lly S2²= 6.2 sje: {(xi - X2: 2.9 hา-) put all this inform afton in ean o we ta 38-31.2 3.5g| 2.92 + bez? 10 14 observed í take q=0.05 sample sample staffstictee taith-2, q to = t10+14–2, O.os to= t22;0.05 1.917 get te = from t table

Page two

p-values 0.0009 1 Right tailed (417.42) - 7:59 Abon Z -2 3 so we Reject to at 5% Here devision:- paralye <a, significant ince level. Concluston: there is enough evidence to suggest that on average juniors perform better on the test than senfors of a bathigh school.

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