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 true. 2. If P -value is greater than (level of significance) reject the null hypothesis. 3. Two samples are dependent if the sample values are matched pairs. 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 30 (n>30) . 5. A claim that two population proportions are equal, each of the two samples must satisfy the requirement that np 5 and nq 5 . 6. In an unpaired samples t-test with sample sizes n1= 21 and n2= 11, the value of t should be obtained at 10 degree of freedom. Section-II (Multiple Choice Questions) (6 marks, 1 Mark Each) 1. Area of the rejection region depends on ... a. Size of b. Size of c. Test-Statistic. d. Number of values 2. A two-tailed test is one where: a. results in only one direction can lead to rejection of the null hypothesis b. negative sample means lead to rejection of the null hypothesis c. results in either of two directions can lead to rejection of the null hypothesis d. no results lead to the rejection of the null hypothesis 3. A decision in a hypothesis test can be made by using a a. P-value b. Critical Value c. A and B d. None of the above 4. When carrying out a large sample test of H0: 0 = 10 vs. Ha: 0 > 10 by using a rejection point, we reject H0 at level of significance the calculated test statistic is: a. Less than z b. Less than - z Page 2 of 4 when c. Greater than z / 2 d. 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. Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 130 acceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 120 acceptable assemblies. The pooled proportion for acceptable assemblies is: a. 250 270 b. 270 250 c. 20 270 d. 270 20 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 Page 3 of 4 (18 marks, 3 Mark Each) 1. A medical researcher claims that less than 20% of American adults are allergic to a medication. In a random sample of 100 adults, 15% say they have such an allergy. Test the researcher's claim at = 0.01. 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 $5.50. 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. Suppose a researcher believes that college faculty vote at a lower rate than college students. She collects data from 200 college faculty and 200 college students using simple random sampling. If 120 of the faculty and 150 of the students voted in the 2016 Presidential election, is there enough evidence at the 5% level of significance to support the researcher's claim? Use the following information to answer questions 5 and 6: Given the following data of two independent samples of normally distributed populations Data Population 1 Population 2 n 23 13 43 41 4.5 5.1 x s 5. Test the claim that 1 2 at the =0.05 level of significance 6. Construct a 95% confidence interval about 12 . Page 4 of 4