Question

3. Test the claim that Statistics students have a different IQ now than when they began the class- Data: A B с DE v N W Now 95 111 102 122 103 110 92 113 108 118 Began 100 105 98 116 103 104 90 112 100 114 3. 4. 5. 6. 7. 8.

Answer 1

Let us denote the difference

d = IQ level now - IQ level at beginning

Let ud denotes the population mean of difference. Hypotheses : To test null hypothesis H. :pld =0 against alternative hypothesis H1 pd #0 This is a two tailed test as alternative hypothesis H contains only #sign. Let à denotes the sample mean of difference, sd denotes the sample standard deviation of difference and n denotes the sample size. Here, d = 3.2000, så = 14.622, sd = 3.8239, n= 10 The test statistic can be written as: vnd – 0.0) te sd which under Ho follows at distribution with n - 1 df. Decision rule / Rejection region : We reject H, at 0.05 level of significance if P-value < 0.05 or if tobs > to.025,n–1 = 2.262157 0.4 0.3 density 2 0.2- 0.1 0.0- t Now, Value of test statistic: The value of the test statistic tobs = (10(3.2000 - 0) 3.8239 2.646326 2.646 associated degrees of freedom = 9 The critical value tcritical = +2.262157 = 2.262 P-value = P(Itn-1] > tobs) = 2 * P(tg < 2.646326) = 2 *0.986682 = 0.026636 0.0266 Conclusion : Since p-value < 0.05 and tobs | > tcritical = 2.262157, so we reject H, at 0.05 level of significance Hence, we can conclude that there is significant difference between two population means.