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Designing a Study
1 Sample Tests of Significance
1 Sample Confidence Interval
2 Sample Confidence Interval
Chi Square Test
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
What does the 1 Sample Test of Significance do?
Compares the difference of a sample statistic from one sample with the mean parameter of a population
100
For a one sample confidence interval the middle value of any interval is equal to what?
The sample statistic
100
2 Sample Confidence Interval for means compares what?
It compares two means
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
What are the requirements for a t-test?
Data must be normally distributed population & σ is unknown
200
What is the formula for a 1 sample confidence interval?
p-hat plus or minus z * square root of (p-hat x 1-p-hat/n)
200
The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a variance of 0.16 m. With a confidence level of 90%, what would the minimum sample size need to be in order for the true mean of the heights to be less than 2 cm from the sample mean?
The sample must be at least 1,083 people.
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
A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score at least 70 on the test. The six students get scores of 62, 92, 75, 68, 83, and 95. Can the professor be at least 90 percent certain that the mean score for the class on the test would be at least 70? Is this a one tailed test? Write the hypothesis and alternative hypothesis.
It is one tailed H0: μ < 70 H a: μ ≥ 70
300
What is standard error?
The standard error is the estimated standard deviation of a statistic
300
The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a variance of 0.16 m. Determine the interval of 95% confidence for the average heights of the population.
n = 400 x = 1.75 σ = 0.4 1 − α = 0.95 zα/2 = 1.96 (1.75 ± 1.96 · 0.4/20 ) → (1.7108,1.7892)
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
A herd of 1,500 steers was fed a special high-protein grain for a month. A random sample of 29 were weighed and had gained an average of 6.7 pounds. If the standard deviation of weight gain for the entire herd is 7.1, what is the likelihood that the average weight gain per steer for the month was at least 5 pounds? Is this a one tailed test or two tailed? Write the Hypothesis and Alternative Hypothesis
One Tailed H0:μ < 5 H0:μ ≥ 5
400
Which of the following statements is true. I. The standard error is computed solely from sample attributes. II. The standard deviation is computed solely from sample attributes. III. The standard error is a measure of central tendency. (A) I only (B) II only (C) III only (D) All of the above. (E) None of the above.
The correct answer is (A)
400
What happens to the width of the intervals when you increase your sample size?
The intervals become narrower
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
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random in which his team scored 5 9, 4, 11, and 8 runs. Is it likely that his team's scores could have come from the national distribution? Assume an alpha level of .05. Is this one tailed or two tailed? Write the Hypothesis and Alternative Hypothesis
Two Tailed H0: μ = 5.7 Ha: μ ≠ 5.7
500
Suppose we want to estimate the average weight of an adult male in Dekalb County, Georgia. We draw a random sample of 1,000 men from a population of 1,000,000 men and weigh them. We find that the average man in our sample weighs 180 pounds, and the standard deviation of the sample is 30 pounds. What is the 95% confidence interval. (A) 180 + 1.86 (B) 180 + 3.0 (C) 180 + 5.88 (D) 180 + 30 (E) None of the above
The correct answer is (A)
500
Suppose that you want to find out the average weight of all players on the football team at Landers College. You are able to select ten players at random and weigh them. The mean weight of the sample of players is 198, so that number is your point estimate. The population standard deviation is σ = 11.50. What is a 90 percent confidence interval for the population weight, if you presume the players' weights are normally distributed?
You are 90 percent certain that the true population mean of football player weights is between 192 and 204 pounds.
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