ST 311 Review Problems

The teacher at Bob's school with the highest performing students gets a $20 gift card. Bob tells his students that a new study states that taking a nap before an exam will improve scores. Because of this, he encourages his students to take a nap before the exam to perform better. During the exam, he includes a question at the end, asking if the student took a nap or not. He finds that 70% of students indicated they took a nap and their average exam score was 5 points higher than thosewho didn't. Which of the following experimental design errors did Bob make?

Bob failed to assign a randomized treatment and control group

Pedro collected a random sample and was able to obtain a 95% confidence interval: (0.546, 0.798). Which of the following would result in a narrower confidence interval? q) Choosing a smaller confidence level b) Increasing the sample size c) Guessing the parameter d) Both A and B

Both A and B

Suppose you have a random sample of 16 NCSU students and would like to construct a 90% confidence interval for the average height of the students. What is the critical value you should use in the confidence interval?

1.753

Tommy wants to find the 90% confidence interval for the mean grade of his math class midterm. There are 13 students in the class. The sample mean is 70 and the sample standard deviation is 3. Which of the following is the correct critical value (i.e. confidence coefficient or multiplier)?

1.782

A biologist would like to analyze the nitrogen content of two specific varieties of red clover plants (Kenland and Marathon) exposed to three strains of Rhizobium: 3D0K1, 3DOK5, and 3DOK7. In preparation for this study, the biologist planted 36 samples of one variety of red clover (Kenland) and 42 samples of the other (Marathon). Assume the biologist has asked you, the researcher, to analyze the data. The biologist wants your recommendation on how to randomize the treatment to the red clover samples, but cautions that the two varieties may respond differently to the treatment. What would you suggest?

A randomized block design, blocking by variety of clover.

Jerry created a 94% confidence interval (0.467,0.695) for a population proportion (all relevant assumptions are satisfied). His boss dismisses Jerry's result and says, "If you are not 100% confident in your sample yet, you should probably try to collect a new one." Is the boss's statement true or false?

False, because 94% refers to the percent of intervals obtained from repeated sampling that contain the population proportion

Is the following statement true or false? The null and alternative hypotheses are written in terms of the sample statistic.

False, because the goal of inference is to draw conclusions about the population parameter, so we design the hypothesis around an "assumed" value

A researcher calculates a 95% confidence interval for a proportion as (.67, .98). Their boss reads their report and says, "There is a 95% probability that the true population proportion is between 0.67 and 0.98." Is the boss's statement true or false?

False: confidence level reflects the proportion of random samples that will result in a confidence interval containing the population proportion.

When test? is it ok to find a 95% confidence interval instead of conducting an 𝛼 = 0.05 level hypothesis

For any hypothesis test with a two-sided alternative hypothesis.

Joon wants to measure the amount of time (mins.) college students spend on their phones. A previous study claimed that the average student spends 240 minutes on their phone each day. Joon randomly samples 200 students and obtains a sample mean of 200 mins. Which of the hypotheses would be the correct null and alternative hypothesis if Joon wanted to investigate if there is a difference?

H0:𝜇=240vsHa: 𝜇 ≠ 240

Which of the following is true about confidence intervals?

The purpose of a confidence interval is to learn about the population parameter.

A biologist would like to analyze the nitrogen content of two specific varieties of red clover plants (Kenland and Marathon) exposed to three strains of Rhizobium: 3D0K1, 3DOK5, and 3DOK7. In preparation for this study, the biologist planted 36 samples of one variety of red clover (Kenland) and 42 samples of the other (Marathon). Assume the biologist has asked you, the researcher, to analyze the data. What are the treatments?

The three strains of Rhizobium, 3D0K1, 3DOK5, and 3DOK7.

In 2009, withering of a large number of crops were ultimately traced to contamination by the pesticide of a certain brand. The manufacturer now claims that the pesticide is safe, but before it can be released, it must be tested. The treatments would be ordinary-size portions of pesticide: the new one from the company (the test pesticide) and one that was certified safe (perhaps the ones that has been used in the past with no issues). The response would be a crop scientist's assessment of the health of crops harvested. Identify the confounding variable.

The weather conditions under which the crops were sown and harvested

Vaidehi believes that how people nap has been changed by the pandemic and working from home. Prior to the pandemic, it is believed that people, on average, napped for 120 minutes each week. She randomly samples 150 people and obtains a sample mean of 160 minutes napped per week. Which set of hypotheses below can be used to investigate the question: Has the mean number of minutes napped per week increased since the pandemic started?

𝐻0:𝜇 = 120 𝑣𝑠. 𝐻𝑎:𝜇 >120

We have conducted a survey where we took a random sample of 400 subjects. We would like to create an 85% confidence interval for a population proportion. Which of the following would be the appropriate confidence coefficient (i.e. multiplier, critical value) for this confidence level?

1.44

We decided to construct a 99% confidence interval for the true proportion of NCSU undergraduates who are in the College of Sciences from a random sample of 500 NCSU undergraduates. The resulting interval is (0.083, 0.157). Which of the following is a correct interpretation of 99% confidence?

About 99% of all confidence intervals constructed in this way will contain the true proportion of NCSU undergraduates who are in the College of Sciences.

Which of the following is NOT true of 95% confidence intervals? (select one)

After we take a random sample and compute a confidence interval from that sample, there is a 95% probability that the true parameter lies in our computed confidence interval.

A hypothesis is conducted to test the following hypotheses: 𝐻0:𝜇=10 𝑣𝑠.𝐻𝑎:𝜇≠10 A sample of size 50 is randomly selected and a p-value is calculated to be 0.048. Which of the following is correct? a) The area under the null distribution that is as or more extreme than the observed sample statistic is 0.048. b) If a 95% confidence interval for the mean is calculated, the interval will not include 10. c) 0.048 is calculated assuming the null hypothesis 𝐻0 is true. d) All of them are correct.

All of them are correct.

Joe and Charlie would like to estimate the average weight of the NCSU students and construct a corresponding 95% confidence interval. Joe collects a random sample of 50 students, while Charlie only finds 20 students randomly and asks for their weight. What is the relationship between the critical values (i.e. confidence coefficients) Joe and Charlie use?

Charlie's critical value is larger.

Which of the following statements is FALSE regarding matched-pair designs:

Each pair must have two unique subjects

If p-value is greater than the significance level, we

Fail to reject the null hypothesis, because it is NOT unlikely to observe the sample statistic assuming the null hypothesis is true.

Samir is trying to test the effectiveness of a new pain relief drug for patients who fractured their backs. He initially split 400 patients into two groups randomly, with one group receiving the placebo and one receiving the new drug. However, he saw his friend was in the placebo group and decided to swap one patient receiving the drug with his friend. He then hires one of the scientists who created the drug to record results. Which of the following experimental problems does Samir NOT have?

Hawthorne Effect

In a manufacturing process, let p be the constant probability of an item being defective. The managers would like to know information about p. From a randomly selected sample of size 100, they obtained a 95% confidence interval (0.0186, 0.0394) for p. Which of the following is TRUE about the margin of error (MOE)?

If they increase the sample size, the MOE will decrease.

Medical researchers have concluded that the effect of a new drug is statistically significant based on the result of a hypothesis test. Suppose the test has been carried out correctly, and all the assumptions were satisfied. Which of the following statements is true?

It is possible that the new drug is actually not effective.

Jung-Ying is a diabetic patient and is part of a clinical trial testing a new type of glucose level control medication. It requires her to take a pill twice a day, 12 hours apart. Halfway through the trial, she feels that the medication isn't working as well as her old medication and decides to take her old medication alongside the clinical trial medication. She doesn't report to the research scientists that she is taking both medications and continues to report her glucose levels. What experimental problem does this describe?

Non-adherence

A researcher wishes to study the relationship between social media use and anxiety. They ask participants to record their usage (in minutes per day) of social media, and their daily anxiety levels. What type of study is described above?

Observation, because the researcher is not intervening in the participants social media use.

In hypothesis test of single proportion, we always reject the null hypothesis when:

P-value is less than the significance level 𝛼 which depends on the context.

Which of the following is true about p-values?

P-value is the probability of observing a test statistic as or more extreme than the one we observed, assuming the null hypothesis is true

If a p-value is smaller than the significance level, we

Reject the null hypothesis, because it is unlikely to observe the sample statistic assuming the null hypothesis is true.

One goal of statistical inference is to:

Select a representative sample from which we can find a statistic to make inferences on the population parameter

Why is it important to use a representative sample?

So that any inference done is trustworthy with respect to the population.Why is it important to use a representative sample?

A biologist would like to analyze the nitrogen content of two specific varieties of red clover plants (Kenland and Marathon) exposed to three strains of Rhizobium: 3D0K1, 3DOK5, and 3DOK7. In preparation for this study, the biologist planted 36 samples of one variety of red clover (Kenland) and 42 samples of the other (Marathon). Assume the biologist has asked you, the researcher, to analyze the data. What would you use for the explanatory and response variables?

The explanatory variable is the Rhizobium, with the three levels 3D0K1, 3DOK5, and 3DOK7. The response variable is the nitrogen content

A crop scientist is conducting research with a drought resistant corn hybrid. She is interested in determining if using fertilizer X will increase yield. She prepares 28 single acre plots and randomly assigns 14 to have normal soil while the other 14 are planted with fertilizer X. The resulting average yield for each group of 14 plots was recorded. Which of the following is NOT correct?

This is best described as an observational study.

Confidence intervals are better to report than just the sample statistic

True, because confidence intervals provide a range of values that we believe will include the population parameter.

The null and alternative hypotheses are written in terms of the population parameter of interest.

True, because the goal of inference is to draw conclusions about the population parameter, even if we can never calculate it.

Suppose we conduct a study on how many hours of wakefulness result from drinking one cup of coffee, and we find that a 95% confidence interval for the mean hours of wakefulness after one cup of coffee is (2.8, 3.4). How would we interpret this confidence interval?

We are 95% confident that the true mean hours of wakefulness after one cup of coffee is in (2.8, 3.4).

Which of the following is true about the margin of error?

he margin of error does not account for sampling bias.

We are able to perform statistical inference because

the sample statistics have a predictable distribution.