3 week 9-week 11 Student Full Name:___________________________________ . Student ID:__________________________________________ . CRN No:____________________________________________ . Branch: _____________________________________________. Total Points True/False ____/6 Short Answer ____/18 Total ____/30 STATISTICS MCQ ____/6 (STAT-101) Good Luck STATISTICS (STAT-101) Marks- 30 Answer all the Questions on the same question paper. Section-I State whether the following statements are True or False. (6 marks, 1 Mark Each) 1. A type I error is the mistake of rejecting the null hypothesis when it is actually false. 2. Two samples are independent if the sample values selected from one population are not related to the sample values from the other population. 3. The null hypothesis (denoted by H0) is a statement that the value of a population parameter is equal to some value. 4. In case of hypothesis testing for a sample, the t statistic is used if is not known and sample size n is greater than 5 (n>5) 5. A claim that two population proportions are equal, each of the two samples must satisfy the requirement that np 30 and nq 30 . 6. In an unpaired samples t-test with sample sizes n1= 21 and n2= 11, the value of t should be obtained at 32 degree of freedom. Section-II (Multiple Choice Questions) 1. If p-value < , then A. Reject H0 B. Accept H0 C. Reject H1 D. All the above 2. (6 marks, 1 Mark Each) The MEAN of the Student t_distribution is A. equal to 0 B. less than 1 C. less than 0 D. greater than 1 3. A decision in a hypothesis test can be made by using a : 1. P-value 2. Critical Value 3. A and B 4. None of the above 4. When carrying out a large sample test of H 0: 0 = 10 vs. H: 0 > 10 by using a rejection point, we reject H0 at level of significance the calculated test statistic is: 1. Less than z Page 2 of 5 when 2. Less than - z 3. Greater than z / 2 4. Greater than z 5. A randomly selected sample of 500 college students was asked whether they had ever used the drug Ecstasy. Sixteen percent (16% or 0.16) of the 500 students surveyed said they had. Which one of the following statements about the number 0.16 is correct? A. It is a population proportion. B. It is a margin of error. C. It is a sample proportion. D. It is a randomly chosen number. 6. Sample sizes n1 = 100, n2 = 100 and numbers x1 = 39, x2 = 41 of successes to find the pooled estimate p 1. 0.4 2. 0.8 3. 0.36 4. 0.48 Part-II (Multiple Choice Questions) MCQ 1 2 3 4 Answer s (6 marks, 1 Mark Each) 5 6 Section -III Answer the following Essay Type Questions (18 marks, 3 Mark Each) 1. Suppose the national unemployment rate is 3%. In a survey of n = 450 people in a rural Wisconsin county, 22 people are found to be unemployed. County officials apply for state aid based on the claim that the local unemployment rate is higher than the national average. Test this claim at the .05 significance level. Page 3 of 5 2. Suppose we would like to determine if the typical amount spent per customer for dinner at a new restaurant in town is more than $20.00. A sample of 49 customers over a three-week period was randomly selected and the average amount spent was $22.60. Assume that the standard deviation is known to be $7.50. Using a 0.05 level of significance, would we conclude the typical amount spent per customer is more than $20.00? 3. The scores on an aptitude test required for entry into a certain job position have a mean at most 500. If a random sample of 36 applicants have a mean of 546 and a standard deviation of 120, is there evidence that their mean score is different from the mean that is expected from all applicants?. Use a 0.05 level of significance. 4. The table show the number satisfied in their work in a sample of working adults with a college education and in a sample of working adults without a college education. Do the data provide sufficient evidence that a greater proportion of those with a college education are satisfied in their work? Use a significance level of = 0.05 to test the claim that p1 < p2. College Education Number satisfied in their 12 work Number in sample 46 No College Education 27 43 Q. 5 & 6.Use the following information to answer Questions 5 and 6: Given the following data of two independent samples of normally distributed populations Page 4 of 5 Data Population 1 Population 2 n 23 13 43 41 4.5 5.1 x s A. Test the claim that 1 2 at the =0.05 level of significance B. Construct a 95% confidence interval about 12 . Page 5 of 5