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Designing a Study
Inference for Means and Errors
Descriptive Statistics
Sampling Distributions
Nope
100
The primary reason for using blocking when designing an experiment is to reduce (A) variation (B) the need for randomization (C) bias (D) confounding (E) the sensitivity of the experiment
A Blocking groups together subjects that are similar and thus reduces variability that is attributable to the differences between the blocks.
100
Which sample size and significance level will give a test of highest power? (A) n = = 25, 0.01 α (B) n = = 25, 0.05 α (C) n = = 50, 0.10 α (D) n = = 50, 0.05 α (E) n = = 50, 0.01 α
(C) n = = 50, 0.10 α
100
If the largest value of a data set is doubled, which of the following is false? (A) The mean increases. (B) The standard deviation increases. (C) The interquartile range increases. (D) The range increases. (E) The median remains unchanged.
Median and IQR are resistant, so they do not change.
100
If heights of 3rd graders follow a normal distribution with a mean of 52 inches and a standard deviation of 2.5 inches, what is the z score of a 3rd grader who is 47 inches tall? (A) -5 (B) -2 (C) 2 (D) 5 (E) 26.2
B Distractors include switching the order of x and μ , and forgetting to divide by the standard deviation.
100
What is the formula for a Chi Square Test?
(Observed - Expected)^2 / Expected
200
A group of 420 college students are enrolled in a blind taste test. The school’s food service wants to see if they can improve the taste of their lattes. They decide to try two types of coffee beans (Arabica and Robusta); three types of syrup (vanilla, hazelnut, and mocha); and two types of milk (soy and low fat). The best combination of ingredients is sought. The latte experiment will have (A) 2 factors, 7 levels, and 420 treatments (B) 2 factors, 3 levels, and 12 treatments (C) 3 factors, 7 levels, and 420 treatments (D) 3 factors, 12 levels, and 420 treatments (E) 3 factors, 7 levels, and 12 treatments
E Three factors (coffee, syrup, milk), 7 levels (2 choices of coffee, 3 choices of syrup, 2 choices of milk), and 2× 3× 2 = 12 combinations
200
A t-test should not be used to conduct a hypothesis test for a mean if which of the following is true? (A) The sample size was only 20. (B) The standard deviation of the population was unknown. (C) The data was obtained by random sampling. (D) A histogram of the data was strongly skewed left. (E) A boxplot of the data showed no outliers.
D Extreme skewness is an indicator of nonnormality of the population.
200
A professor scaled (curved) the scores on an exam by multiplying the student’s raw score by 1.2, then adding 15 points. If the mean and standard deviation of the scores before the curve were 51 and 5, respectively, then the mean and standard deviation of the scaled scores are respectively: (A) 76.2 and 21 (B) 76.2 and 6 (C) 76.2 and 5 (D) 61 and 6 (E) cannot be determined without knowing if the scores are normally distributed
B Don’t add 15 when transforming the standard deviation.
200
Suppose that a normal model describes the acidity (pH) of rainwater, and that water tested after last week’s storm had a z-score of 1.8. This means that the acidity of the rain (A) had a pH 1.8 higher than average rainfall. (B) had a pH of 1.8. (C) varied with standard deviation 1.8 (D) had a pH 1.8 standard deviations higher than that of average rainwater. (E) had a pH 1.8 times that of average rainwater.
D z score is number of standard deviations from mean
200
What is the formula for degrees of freedom for a Goodness of Fit test?
(Number of categories) - 1
300
A student organization wants to assess the attitudes of students toward a proposed change in the hours the library is open. They randomly select 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors to survey. This situation is described as (A) a stratified random sample (B) a simple random sample (C) a convenience sample (D) a systematic random sample (E) an observational study
(A) a stratified random sample
300
Which of the following is the correct interpretation of a p-value of 0.003? (A) The probability of seeing the observed statistic or something more extreme, if the alternative hypothesis is true, is 0.003. (B) The probability of seeing the observed statistic or something more extreme, if the null hypothesis is true, is 0.003. (C) The probability of failing to reject the null hypothesis is 0.003. (D) The probability that the null hypothesis is true is 0.003. (E) The probability that the alternative hypothesis true is 0.003.
B The p-value describes the chance that the observed data belongs to the given distribution.
300
The five-number summary for scores on a statistics exam is 35, 68, 77, 83, 97. In all, 196 students took the test. About how many had scores between 77 and 83? (A) 6 (B) 39 (C) 49 (D) 98 (E) It cannot be determined from the information given.
(C) 49
300
In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval? (A) 1084 to 1216 pounds (B) 1106 to 1150 pounds (C) 1106 to 1194 pounds (D) 1128 to 1172 pounds (E) 1150 to 1194 pounds
3. C Distractors include adding/subtracting 1 or 3 standard deviations instead of 2.
300
What is the purpose of a Chi Square Test?
The purpose is to see whether observed experimental data is a 'good fit' with theoretical expected results.
400
Twenty men and 20 women with migraine headaches were subjects in an experiment to determine the effectiveness of a new pain medication. Ten of the 20 men and 10 of the 20 women were chosen at random to receive the new drug. The remaining 10 men and 10 women received a placebo. The decrease in pain was measured for each subject. The design of this experiment is (A) completely randomized with one factor, gender (B) completely randomized with one factor, drug (C) randomized block, blocked by drug and gender (D) randomized block, blocked by gender (E) randomized block, blocked by drug
D This is not a completely randomized design because the treatment group was not chosen randomly from a list of all 40 volunteers. Since the treatment group was chosen randomly from 2 separate lists (males and females), this study is blocked by gender.
400
Compare the standard normal distribution to the t-distribution. Which of the following statements are true? I. Both distributions have a mean of zero. II. Both distributions are symmetric and bell-shaped. III Both distributions have approximately 68% of the data within one standard deviation of the mean.
I and II only
400
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The correct answer is to choose another question.
400
The height of male Labrador Retrievers is normally distributed with a mean of 23.5 inches and a standard deviation of 0.8 inches. (The height of a dog is measured from his shoulder.) Labradors must fall under a height limit in order to participate in certain dog shows. If the maximum height is 24.5 inches for male labs, what percentage of male labs are not eligible? (A) 0.1056 (B) 0.1250 (C) 0.8750 (D) 0.8944 (E) 0.9750
A Distractor is finding eligible labs under the height limit instead of those who are not eligible.
400
The p-value of a chi-square test is (0.0003). Write a conclusion using this p-value at the .05 significance level.
Since the P-value (0.0003) is less than the significance level (0.05), we cannot accept the null hypothesis. Thus, we conclude that there is a relationship between gender and voting preference.
500
The state would like to evaluate the usefulness of a program to randomly test high school athletes for steroid use. Initially, a state agency will test athletes in all 20 schools in Fort Worth, randomly selecting 3 athletes from each school. Is this a simple random sample of student athletes in Fort Worth? (A) Yes, because athletes will be chosen at random. (B) Yes, because each athlete is equally likely to be chosen. (C) Yes, because stratified sampling is a special case of simple random sampling (D) No, because not all possible groups of 60 athletes could be in the sample. (E) No, because a random sample of Ft. Worth schools is not chosen.
(D) No, because not all possible groups of 60 athletes could be in the sample.
500
Suppose a machine that makes pegs to be used in holes to hold furniture parts together is malfunctioning, but the manufacturer doesn’t know it. A quality control test is conducted bimonthly with the null hypothesis stating that the machine works properly. The p-value of the most recent test was 0.185. What probably happens as a result of this test? (A) The test correctly fails to reject HO . (B) The test correctly rejects HO . (C) HO is rejected, resulting in a Type I error. (D) HO is not rejected, resulting in a Type I error. (E) HO is not rejected, resulting in a Type II error.
E A p-value greater than any alpha results in a failure to reject HO, yet because the problem states that the machine is malfunctioning, we know that HO is false. Failing to reject a false HO is a Type II error.
500
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The correct answer is to choose another question.
500
The heights of mature pecan trees are approximately normally distributed with a mean of 42 feet and a standard deviation of 7.5 feet. What proportion of pecan trees are between 43 and 46 feet tall? (A) 0.1501 (B) 0.2969 (C) 0.4470 (D) 0.5530 (E) 0.7031
A Distractors are finding proportion of trees under or over 43 or 46 feet instead of those between 43 and 46 feet.
500
What are all the requirements to perform a Chi-Square Test?
1. All expected counts are at least 1 2. No more than 20% of expected counts are less than 5