1. True or False. Justify for full credit. (a) A is an event, and A c is the complement of A, then P(A OR A c ) = 0. (b) If the variance of a data set is 0, then all the observations in this data set must be identical. (c) If a 95% confidence interval for a population mean contains 1, then the 99% confidence interval for the same parameter must contain 1 (d) When plotted on the same graph, a distribution with a mean of 60 and a standard deviation of 5 will look more spread out than a distribution with a mean of 40 and standard deviation of 8. (e) In a right-tailed test, the value of the test statistic is 2. The test statistic follows a distribution with the distribution curve shown below. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.
2. Choose the best answer. Justify for full credit. (a) A study was conducted at a local college to analyze the average GPA of students graduated from UMUC in 2015. 100 students graduated from UMUC in 2015 were randomly selected and the average GPA for the group is 3.5. The value 3.5 is a (i) statistic (ii) parameter (iii) cannot be determined (b) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is (i) interval (ii) nominal (iii) ordinal (iv) ratio (c) In a career readiness research, 100 students were randomly selected from the psychology program, 150 students were randomly selected from the communications program, and 120 students were randomly selected from cyber security program. This type of sampling is called: (i) cluster (ii) convenience (iii) systematic (iv) stratified
3. Choose the best answer. Justify for full credit. (a) A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50 subjects in it. The subjects were followed for 12 months. Weight change for each subject was recorded. You want to test the claim that the mean weight loss is the same for the 10 programs. What statistical approach should be used? (i) t-test (ii) linear regression (iii) ANOV A (iv) confidence interval (b) A STAT 200 instructor teaches two classes. She wants to test if the variances of the score distribution for the two classes are different. What type of hypothesis test should she use? (i) t-test for two independent samples (ii) t-test for matched samples (iii) z-test for two samples (iv) F- test
4. The frequency distribution below shows the distribution for IQ scores for a random sample of 1000 adults. ( Show all work. Just the answer, without supporting work, will receive no credit.) (a) Complete the frequency table with frequency and relative frequency. Express the relative frequency to three decimal places. (b) What percentage of the adults in this sample has an IQ score of at least 110? (c) Does this distribution have positive skew or negative skew? Why or why not?
5. Answer each question based on the given information, and e xplain your answer in each case. (a) What is the interquartile range in the grade distribution? (b) Which score band has the most students? (i) 20-60 (ii) 60 - 85 (iii) 80 - 100 (Iv) Cannot be determined (c) How many students are in the score band between 60 and 70?
6. Consider selecting one card at a time from a 52-card deck. What is the probability that the first card is an ace and the second card is also an ace? (Note: There are 4 aces in a deck of cards) ( Show all work. Just the answer, without supporting work, will receive no credit.) (a) Assuming the card selection is without replacement. (b) Assuming the card selection is with replacement