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Name:_________________________
Stat 303: Section 506
Fall 2006
Form A
Instructor: Elizabeth Young
Instructions:
1.) Don’t EVEN open this until I tell you. (Meanwhile, read the rest of the
instructions.)
2.) Be SURE to mark your Form on the scantron!
3.) 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.”
4.) 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.
5.) You have 50 minutes to finish this exam. It is worth 15% of your final
grade.
6.) Turn in your cheat sheet and z-tables inside this form. Put the scantron in
a separate stack.
1.) In a hypothesis test for Ho: μ = 0.04 vs. Ha: μ ≠ 0.04, it was found from a sample of 36 that x = 0.06, and it was known that σ = 0.02. Calculate the test statistic for this test. A.) 1 B.) 0 C.) 0. D.) 6 E.) 0. 2.) Which of the following is true for confidence intervals? A.) Our confidence interval formula is appropriate for simple random samples, stratified random samples, and cluster samples. B.) If the original population is normally distributed, then our confidence interval formula is always valid for any sample size. C.) Undercoverage and nonresponse bias are accounted for when we create confidence intervals. D.) Confidence intervals are not strongly affected by the presence of outliers. E.) If the size of the population increases, the width of the confidence interval decreases. 3.) In a hypothesis test of Ho: 5 vs. Ha: μ ≠ 5, a test statistic of 0.8023 was found. Calculate the p-value for this test. A.) 0. B.) 0. C.) 0. D.) 0. E.) 0. 4.) A consumer report journal wanted to find out whether different brands of microwaves pop different numbers of kernels per bag. It is known that the former microwave brand pops 1500 kernels in 3 ½ minutes. What hypotheses about the new microwave band should be set up? A.) Ho: μ ≤ 1500 Ha: μ > 1500 B.) Ho: μ = 1500 Ha: μ ≠ 1500 C.) Ho: μ ≤ 3 ½ Ha: μ > 3 ½ D.) Ho: x ≤ 1500 Ha: x > 1500 E.) Ho: x = 3 ½ Ha: x ≠ 3 ½ 5.) Which of the following BEST describes a sampling distribution? A.) The probability that we obtain the statistic in repeated random samples of the same size from the same population B.) The mechanism that determines whether the randomization was effective C.) The distribution of all values of a statistic in all possible samples of the same size from the same population D.) The distribution of all possible samples from the same population
10.) A doctor wants to test whether the blood pressure rate for middle-aged males is higher on average than that for the general population of men. Suppose in reality, the blood pressure for middle-aged men actually is higher. The doctor found a p-value of 0.3645, and wants to use an α) * 100% of the time. of 0.06. Which of the following statements is true? A.) The doctor made a Type I error: he rejected the null hypothesis when he shouldn’t have. B.) The doctor made a Type II error: he didn’t reject the null hypothesis when he should have. C.) The doctor didn’t make any mistake at all; he made the correct decision about whether to reject. D.) If he had had a larger sample size, his test would have been less powerful. E.) Two of the above are true. 11.) Suppose X has a mean of 3 and standard deviation 5, while Y has a mean of 5 and standard deviation 6. What is the distribution of (^) X Y , where (^) X and (^) Y are the sample means from samples of 45 each? A.) (^) X Y ~N(-2, 1.28^2 ) B.) (^) X Y ~ N(-2, 7.81^2 ) C.) (^) X Y ~N(-2, 0.494^2 ) D.) (^) X Y ~N(-2, 1.16^2 ) E.) We cannot determine the distribution, since we don’t know the original distributions of X and Y. 12.) Given the three confidence intervals for μ below, what is the range for the p-value for testing the hypothesis Ho: μ = 16 vs. Ha: μ ≠ 16? 90%: (13.68,14.96) 95%: (13.56, 15.08) 99%: (13.04,15.60) A.) p-value > 0. B.) 0.05 < p-value < 0. C.) 0.01 < p-value < 0. D.) p-value < 0. E.) We need a test statistic to calculate p-value. 13.) Which of the following is true about probability? A.) Since probabilities are normally distributed, they can be negative. B.) Probability distributions are for numeric data since you can’t find a mean for categorical data. C.) Probability distributions are always normal in shape. D.) Every probability must be nonnegative, but no more than 1. E.) Two of the above are true.
14.) For which value(s) of π will the rule for using the normal approximation hold, if we take a sample of size 30? A.) 0. B.) 0. C.) 0. D.) Two of the above. E.) All we need to have is a sample of size of at least 30, so it will hold for any value of π. 15.) Ladies’ Home Journal recently asked 529 women whether how a woman speaks or how she dresses was more important. If the true proportion of women who believe how a woman speaks is more important is 0.80, what is the probability that the sample proportion is 0.81 or greater? A.) 0. B.) 0. C.) 0. D.) 0. E.) 0. 16.) Which of the following is true? (Think about the Central Limit Theorem.) A.) Averages are more variable than individual observations. B.) Averages are less normal than individual observations. C.) If a population is skewed, then a larger sample size is required for a sample average to be normal than if the population were symmetric. D.) If a population is normally distributed, we only need n ≥ 20 or so in order for a sample average to be pretty close to normally distributed. E.) Two of the above are true. 17.) About 40% of Americans say they are afraid to go out at night because of crime. In a sample of 1050 people, what is the probability that we would find a sample proportion somewhere between 39% and 41%? A.) 0. B.) 0. C.) 0. D.) 0. E.) 0. 18.) If X ~ N(0, 2^2 ), what is P(X > 1.36)? A.) 0. B.) 0. C.) 0. D.) 0. E.) 0.
