Alternate Solution Using the zDest, the probability or proportion of \"The Surgeon\" is: (No. of people liked The Surgeon") (Total no.9)\" viewers) The proportion of people liking \"The Surgeon" is 0'6 Next, calculate the zscore = 11-120 Z-score 7\" '71:\") Where, 1) = Observed Proportion = Q6 pa = Null Hypothesized value = 0.5 n = sample size = 20 Null Hypothesized value = 0.5 (no preference between the two shows) Substituting all the values in the z-score we get, ZSOOl'e = Z = 0.89 Now we should nd the P value based on the zscure. The alternative hypothesis is that the proportion is not equal to 0.5 Looking at the added probability of getting either > positive 0.89 or 10, Alternate Hypothesis + Signs more than n/2 (x - .50)-H = 7- (x-.50)-.50n .50 vn Him # .50 There is a preference in shows If the number of pluses or minuses is less than n/2, the test statistic z is: Step 2: Select the level of significance. Formula #2 Level of significance is .10 as stated in the problem. Sign Test, n > 10, Step 3: Select the test statistic. + Signs Less than n/2 z = (x+.50)-4 _ 7- (x+.50)- .50n 50 Vn The test statistics is: (+) 12 liked "The Surgeon" = 12 > n/2, = 20/2 = 10 we use formula #1 (+) 7 liked "Critical Care" z = (x 1.50)-H 1 had no preference z = (x-.50)-H = 7=- (12-.50)- .50(20) = 0.670 Where u = .50n and o = .50 vn .50 V20 Step 4: Formulate the decision rule. The computed z of 0.670 is smaller than the critical value 1.645. Therefore, the null hypothesis of no difference is rejected at the . 10 significance level. Using the Student's t Distribution, with infinite degrees of freedom, for a two tailed test. This is used because Hi:n # .50 and at . 10 significance level, the critical values are +1.645 and -1.645