Question

The One Sample 2 Test ESP A husband and wife claim that they have a special bond that allows them to communicate by ESP. To test this claim, an researcher puts the husband and wife in separate rooms. The husband is randomly shown one of colors: either blue, red, green, yellow or orange. He then is given 5 seconds to use his ESP to communicate the color to his wife. The wife then has to decide which of the 5 colors she was shown. This process is repeated 900 times. The wife correctly identifies the color 198 out of the 900 times. The rull hypothesis is that she just guessed her husband's answers a. The null hypothesis is that the experiment is like drawing 900 times

Answer 1

As given in the question: The number of times experiment is drawn n=900 The number of times wife correctly identify the color x = 198 The probability of success or correctly identifying the color =- 198 900 = 0.22 The null and the alternative hypothesis be: Ho: p=0.5 H:p > 0.5 (Right-tailed test) Here, p represents the population proportion of correctly identifying the color. The expected value of the sum of the draws = np = 900 x 0.5 = 450 np(1 - p) The standard deviation of the null box = = 900X0.5(1-0.5) = V900X0.5x0.5 P = P(-2) The standard error of the sum of the draws - VP 10.5(1-0.5) V 900 = 0.0167

The value of z test statistic: p(1 – p) Vn 0.22-0.5 10.5(1 -0.5) V 900 -0.28 0.0167 = -16.766 The p-value corresponding to z = -16.766 is less than 0.00001 (By using the standard normal table.)

Part 2: As given in the question: The population mean u = 50 The sample size n=9 The sample mean = 47 The sample standard deviation s = 3 (h) The standard error se The sample size is less than 30 and the population standard deviation is not given. Hence, use t-test here. The t-test for one independent sample is given by: t-i-u se 47-50 1