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Name:____________________________
Stat 303: Section 504
Fall 2008
Instructor: Yogesh Dwivedi
Instructions:
1.) Don’t EVEN open this until I tell you. (Meanwhile, read the rest of the
instructions.)
2.) TURN IN this form, your cheat sheet, and your scantron. Put your name
on everything!
3.) Be SURE to mark your Form on the scantron!
4.) Sign your name on the line on the scantron. With this signature, you
agree to follow the Aggie Honor Code:
“An Aggie does not lie, cheat, or steal or tolerate those who do.”
5.) There are 20 multiple-choice questions, each worth 5 points. Please
mark your answers CLEARLY with a #2 pencil. Multiple marks will be
counted wrong.
6.) You have 50 minutes to finish this exam. It is worth 15% of your final
grade.
7.) Good luck!
Suppose an experimenter wishes to test the hypotheses Ho: μ 1 = μ 2 vs. Ha: μ 1 ≠ μ 2 using the pooled t-test. If SPSS gives the t-value -2.48, with samples of size n1 = 38, n2 = 38, what is a range for the p-value? A.) 0.025 < p-value < 0. B.) 0.05 < p-value < 0. C.) 0.0025 < p-value < 0. D.) 0.005 < p-value < 0. E.) 0.01 < p-value < 0. 2.) The following confidence intervals for π were found. For testing the hypotheses Ho: π = 0.4 vs. Ha: π ≠ 0.4, what is the range for my p-value? 99%: (0.015, 0.447) 96%: (0.059, 0.404) 95%: (0.066, 0.396) 90%: (0.093, 0.369) A.) 0.1 > p-value > 0. B.) 0.05 > p-value > 0. C.) 0.04 > p-value > 0. D.) pvalue < 0. E.) You need a test statistic to determine p-value. 3.) Given Ho: π = 0.5 vs. Ha: π ≠ 0.5, with a sample proportion of 0.63 and a sample of size 50, what are the test statistic and p-value for this test? A.) 1.90 and 0. B.) 1.90 and 0. C.) 1.90 and 0. D.) 1.84 and 0. E.) 1.84 and 0. 4.) Suppose the population is normally distributed is N(3,5^2 ). A sample of size 4 is randomly taken from this population and a 90 % CI is to be constructed. Sample mean was found to 2.45 and sample standard deviation, s = 3.5. Suppose: z^ for 90% CI is 1. t^ for 90% CI is 2. Which one of the following correctly measures 90% confidence interval? A) (2.45 – 1.6453.5/2, 2.45 + 1.6453.5/2) B) (2.45 – 2.3533.5/2, 2.45 + 2.3533.5/2) C) (2.45 – 2.3535/2, 2.45 + 2.3535/2) D) None of the above.
Q9.)
Say instead, we want to know, of the people with feet that are different lengths, are you more likely to have your right foot longer than your left. Which set of hypotheses is correct? Note: πleft is the proportion of people with their left foot longer than their right and μleft is the true average length of people's left foot. A.) Ho: πleft = πright vs Ha: πleft < πright B.) Ho: πright = 0.5 vs Ha: πright > 0. C.) Ho: μleft = μright vs μleft < μright D.) Either A or B E.) Either B or C Q10.) An engineer interested in quality control has just tinkered with a manufacturing machine. Previously, the proportion of defective parts created by the machine had been 0.18; the engineer wants to prove to his boss that the proportion of defective parts has decreased. What hypotheses should he set up? A.) Ho: π ≥ 0.18 vs. Ha: π < 0. B.) Ho: π = 0.18 vs. Ha: π ≠ 0. C.) Ho: π 1 ≤ π 2 vs. Ha: π 1 – π 2 > 0. D.) Ho: μ ≥ 0.18 vs. Ha: μ < 0. E.) Ho: μ = 0.18 vs. Ha: μ ≠ 0. Q11.) When testing a statistical hypothesis, we fail to reject Ho at the α% level if A. Ho is true. B. the hypothesized value under H 0 is less than the sample value. C. α is less than the p-value of the test statistic. D. Exactly two of the above is true. E. None of the above are true. Q12.) Suppose X~N(μ 1 ,3^2 ) and Y~N(μ 2 ,3^2 ). A 95 % CI is to be constructed for μ 1 - μ 2. Sample of size 40 and 60 is drawn from both population X and Y and the following statistics is obtained. Sample Mean Sample Standard Deviation Sample from X of size 40 5 3. Sample from Y of size 60 3.5 3. What would be the critical value for 95% CI used in the confidence interval? A .) 1.
B.) Since sample standard deviation are so close we can pool the standard deviations, thus we use t-distribution with df= 40+60-2 = 98, and critical value for 95% CI will then be 1.990 (rounding down to df=80 since 98 is not on the chart). C.) We use the critical value from t-distribution with df=39, which is 2.042 (rounding down to df=30 since 39 is not on the chart). D.) We use the critical value from t-distribution with df=59, which is 2.009 (rounding down to df=50 since 59 is not on the chart). E.) None of the above. Q13.) Suppose that the data collected from our class survey is a random sample from the entire university. We wish to see if there is evidence that the average amount of television watched for students here is more than 7 hours per week. What would the alternative hypothesis and the decision be for this test if z-statistic was 3.14? (Use 5% significance level) A. Ha: mu > 7, Fail to reject Ho B. Ha: mu >= 7, Reject Ho C. Ha: mu < 7, reject Ho D. Ha: mu < 7, Fail to reject Ho E. None of the above Q14.) Oprah wants to increase revenue. She has a lot of female targeted advertising, so her only outlet is to increase the advertising targeted at males. You need at least a 20% viewing audience to attract advertisers, so she needs to find out if her audience is more than 20% male. What hypotheses should she test? Let F indicate females and M males. A.) Ho. μF = μM vs. Ha: μF ≠ μM B.) Ho. πF = πM vs. Ha: πF > πM C.) Ho. μF = μM vs. Ha: μF > μM D.) Ho. πM =0.20 vs. Ha: πM < 0. E.) Ho: πM =0.20 vs. Ha: πM > 0. Q15.) Which of the following is true about the property of the t distribution? A.) It is always centered at zero. B.) It is always wider than the z distribution C.) It is always symmetric D.) It’s height, at center, increases as the degrees of freedom increases. E.) All of the above are properties of the t distribution.
Use the following to answer questions 18-19: Two statistics professors at two rival schools decide to use IQ scores as a measure of how smart the students at their respective schools are. IQ scores are known to be normally distributed. The two professors will use this knowledge to their advantage. They will randomly select 10 students from their respective schools and determine the students’ IQ scores by means of the standard IQ test. The two professors will use the pooled version of the two sample t test to determine whether the students at the two universities. Let σ 1 and σ 2 be the corresponding population standard deviations. The hypotheses they will test are Ho: μ 1 – μ 2 = 0 versus Ha: μ 1 – μ 2 ≠ 0. Based on the two samples of 10 students, the two professors find the following information: (^111) , 120 , 7 , 11 1 =^2 = 1 = 2 = − − x x s s. Q18.) What is the value of the test statistic? A) 0. B) -0. C) -2. D) -3. Q19.) Suppose the professors had wished to test the hypothesis Ho: μ 1 = μ 2 versus Ha: μ 1 < μ 2. What can we say about the value of the p-value? A) p-value < 0. B) p-value > 0. C) 0.025<p-value<0. D) 0.02<p-value<0. E) None of the above Q20) Suppose a 90% CI for mu is (7.342,8.658). What would the 95% CI be for mu be if z* for 95% is 1.96 and population standard deviation is known to be 4 and the sample taken was of size 100. A) (7.216, 8.784) B) (7.204,8.796) C) (7.023,8.234) D) (7.342,8.658) E) None of the above Q21.) Who is the president of United States of America? A.) John McCain B.) Barack Obama C.) Joe Biden D.) Sarah Pailen E.) George W. Bush
