Homework answers / question archive / ST351 Final Exam Fall 2020 Quiz Instructions Question 18 pts For each of the following statements indicate whether the answer is TRUE or FALSE

ST351 Final Exam Fall 2020 Quiz Instructions Question 18 pts For each of the following statements indicate whether the answer is TRUE or FALSE

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ST351 Final Exam Fall 2020

Quiz Instructions

Question 18 pts

For each of the following statements indicate whether the answer is TRUE or FALSE. 

 

Statement 1. When n is sufficiently large, the sampling distribution of  x ¯ is approximately normal even if the population is not normally distributed.              ["", ""]                          [ Select ]TRUEFALSE  

 

Statement 2. The smaller the p-value, the stronger the evidence is against the alternative hypothesis, H_a.              ["", ""]                          [ Select ]TRUEFALSE

 

Statement 3. The symbols  μ and  σ are characteristics of a sample.              ["", ""]                          [ Select ]TRUEFALSE

 

Statement 4: When n is large the sampling distribution for  p ^is normally distributed with mean p and standard deviation p × ( 1 − p ) n .              ["", ""]                          [ Select ]TRUEFALSE

 

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Question 22 pts

Based on repeated sampling, the probability distribution of a sampled statistic is referred to as the

 

Group of answer choices

sampling distribution.

p-value.

margin of error.

Normal distribution.

 

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Question 32 pts

Which of the following is a general way of interpreting a confidence interval?

Group of answer choices

A 95% confidence interval provides values that the population parameter could be, along with some degree of uncertainty.

A 95% confidence interval provides the probability that the true value of the parameter is inside the interval.

A 95% confidence interval allows you to determine if you've made a type I error.

A 95% confidence interval is the probability of observing a sample like the one we did or something more extreme if the null hypothesis is true.

 

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Question 42 pts

According to the Central Limit Theorem, when sample size goes from n = 50 to n = 200, what happens to the standard deviation of sampling distribution as the sample size increases as well as the shape of the distribution?

Group of answer choices

o The standard deviation stays the same and the shape becomes more skewed left.

o The standard deviation becomes smaller and the shape becomes more skewed left.

o The standard deviation becomes smaller, and the shape becomes closer to normal.

o The standard deviation becomes larger, and the shape becomes closer to normal.

 

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Question 510 pts

Use the following for the next 4 questions. New heat lamps are reported to have the mean lifespan of 100 hours with a standard deviation of 15 hours. Before replacing their current lamp to the new heat lamps for the university, OSU decided to test whether the mean lifetime is equal to 100 or not by sampling 36 heat lamps. They turned them on and recorded the time, in hours, until each lamp failed. The sample provided a mean lifespan is 105.1 hours.

a) What set of hypotheses are correct for this problem?              ["", "", ""]                          [ Select ]SET 1SET 2SET 3

SET 1 - H₀: µ = 100 hours , H_a: µ < 100 hours

SET 2 - H₀: µ = 100 hours , H_a: µ > 100 hours

SET 3 - H₀: µ = 100 hours , H_a: µ  ≠ 100 hours

b) If we assume the null hypothesis to be true, the average of the distribution of sample means,  μ x ¯, from a sample size of 36 is              ["", "", "", ""]                          [ Select ]15115100105.1 . 

 

c ) According to the Central Limit Theorem, the standard deviation of the distribution of the sample means is              ["", "", "", ""]                          [ Select ]1151562.5 . 

 

d) What is the approximate probability of observing a sample mean of 105.1 or more from the distribution of sample means, again assuming that the null hypothesis is true? (Use the 68-95-99.7 rule to approximate this probability. It may be helpful to sketch out the distribution)

             ["", "", "", ""]                          [ Select ]0.680.0250.9750.16 . 

 

 

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Question 62 pts

In general when calculating any confidence interval what action will increase the width of the interval?

Group of answer choices

Increasing the point estimate.

Increasing the sample size.

Increasing the level of confidence.

All choices will result in wider confidence intervals.

 

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Question 72 pts

Complete the sentence with the correct response. 

Assuming the null is true, the probability the test statistic would take a value at least as extreme than the one actually observed is the              ["", "", "", ""]                          [ Select ]sampling distributionp-valuemargin of errorNormal distribution   of the test.

 

 

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Question 82 pts

In planning a study of birth weights of babies whose mothers did not see a doctor before delivery, a researcher states the hypotheses as

H 0 : x ¯ = 1000 g r a m s H a : x ¯ < 1000 g r a m s

What is wrong with the hypotheses as they are written?

 

Group of answer choices

Nothing is wrong with the hypotheses.

Hypotheses are about the population mean of birth weights. Therefore the symbol should  μ be used instead of  x ¯.

Birth weight is categorical. Therefore the symbol used should be  p ^ a instead of  x ¯.

The alternative hypothesis should contain the equal sign and the null should have the “less than” symbol.

 

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Question 92 pts

Use the following to fill in the answers for the statements below. A manufacturer or metal gadgets wanted to run a few tests to determine if their machine working properly with few defects. They randomly sampled 1000 gadgets produced over the course of a week and determined if there was a defect on each sampled gadget. Quality control used the following hypotheses

H₀: p = 0.05 ; The proportion of defective gadgets is at the acceptable level of 0.05.

H_a: p > 0.05 ; The proportion of defective gadgets is greater than the acceptable level of 0.05 and the machine will need repairs.

They use a significance level of 0.05. Consider the following outcomes of the study. Based on the description of the truth (only the Data Gods really know) and the decision made from the hypothesis test, match the type of error or lack of one. 

Outcome 1. The test results in a p-value of 0.02. Quality control decides that there is evidence the machine needs repairs, but in reality the matching is working just fine. This outcome results in              ["", "", ""]                          [ Select ]a Type I errora Type II errorthe correct decision with no error. . 

Outcome 2. The test results in a p-value of 0.35. Quality control decides there is not enough evidence to suggest the machine needs repairs, but reality the machine is not working properly and needs to be fixed. This outcome results in              ["", "", ""]                          [ Select ]a Type I errora Type II errorthe correct decision with no error. . 

Outcome 3. The test results in a p-value of 0.35. Quality control decides there is not enough evidence to suggest the machine needs repairs and in reality the machine is working just fine and truly does not need repairs. This outcome results in              ["", "", ""]                          [ Select ]a Type I errora Type II errorthe correct decision with no error. . 

 

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Question 108 pts

Match the scenario with the the appropriate test. Each test can only be used once. 

Group of answer choices

Learning Success Center is conducting an experiment to determine whether intensive tutoring (covering a great deal of material in a fixed amount of time) is more effective than paced tutoring (covering less material in the same amount of time). Two randomly chosen groups of students are tutored separately and then administered proficiency tests after 8 weeks. Use a significance level of α < 0.05. What procedure will best test the performance difference in the average grades of the two tutoring methods?

                                                [ Choose ]Two-Sample t-testOne proportion z-testOne sample t-test

A running shoe company claims their shoe will withstand an average lifetime distance of 600 miles. For quality assurance purposes, they randomly sample 5 shoes from each batch and test their wear through simulation. If the sample provides evidence the entire batch has a mean below 600 miles, they will need to further investigate the batch of shoes. Otherwise, they will prepare them for market. They know the population of all wear lifetimes is normal. The sample yielded an average of 535 miles and a standard deviation of 60 miles. What type of test is appropriate for this scenario?

                                                [ Choose ]Two-Sample t-testOne proportion z-testOne sample t-test

In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists wants to test a new medication to see if it has either a positive or negative effect on intelligence or no effect at all. A sample of 74 participants who have taken the medication has a mean of 140. What type of test is appropriate for this scenario?

                                                [ Choose ]Two-Sample t-testOne proportion z-testOne sample t-test

 

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Question 112 pts

Use the following to answer the next 3 questions.

The state of Oregon would like to test whether the average GPA of college students is different than 3.2 or not for scholarship purposes. They take a random sample of 1000 college students in Oregon. Here is the summary statistics.

Sample mean,  x ¯	3.18
Sample size, n	10,000
Sample standard deviation, s	0.46

 

**Note the graph title says sample size of 1000, but it should read 10,000

Which of the following is a FALSE description of the data?

Group of answer choices

The GPA is heavily right skewed.

Most Oregon students tend to have a GPA near 3.2

The range of GPAs is about 2.7.

A majority of GPAs is grater than 2.5.

 

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Question 1210 pts

Refer to the information in the previous problem.

Suppose we test like to test the hypotheses,

H₀ : μ = 3.2  vs.  H_a : μ  ≠ 3.2

with a significance level of  α = 0.05. Which of the following methods are a valid way to test the hypotheses?

For each of the following methods indicate whether they are a valid way to test the hypotheses. In other words, is the method described an appropriate way of finding a p-value and trusting the conclusion is a correct conclusion considering the data.

Method 1. Using our experience on the subject, we try to guess what the p-value is likely to be.  

Method 1 is              ["", ""]                          [ Select ]a validNOT a valid   procedure. 

 

Method 2. Take 10000 samples from the population of all Oregon college students, for each sample record the mean. Find the p-value by determining the proportion of these means that are greater than 3.2.

Method 2 is              ["", ""]                          [ Select ]a validNOT a valid   procedure. 

 

Method 3. Calculate the 95% confidence interval for  μ , if the null hypothesized value does not fall within the interval then we can reject the null hypothesis.

Method 3 is              ["", ""]                          [ Select ]a validNOT a valid   procedure.

 

Method 4. Perform a one sample z-test for the proportion of GPAs greater than 3.2

Method 4 is              ["", ""]                          [ Select ]a validNOT a valid   procedure.

 

Method 5. To solve for the p-value, they can calculate a t-test statistic and degrees of freedom and find the area under the t-distribution curve that is more unusual than the calculated test statistic.

Method 5 is              ["", ""]                          [ Select ]a validNOT a valid   procedure. 

 

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Question 132 pts

Recall that the alternative hypothesis is H_a:  μ  ≠ 3.2 and the sample mean was found to be 3.18 from 10,000 college students from across Oregon. The p-value was determined to be less than 0.0001. With this in mind, which of the following statements is correct?

Group of answer choices

We have found statistical significance but no practical significance.

We have found both statistical and practical significance.

We have found no statistical significance but we do see practical significance in the data.

This study does not have any statistical or practical significance.

 

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Question 142 pts

A Portland high school wanted to see if reading test scores have changed in the past 30 years by testing a random sample of 25 students to see whether there is a significant change from the average score of 78 thirty years ago. The sample yields a mean and standard deviation of 84 and 8 respectively.

What is the unknown parameter of interest in this example?

Group of answer choices

The population standard deviation σ.

x ¯ the sample average score of 25 students.

μ the average reading score of students in that Portland high school.

None of the above.

 

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Question 152 pts

Using the information in the previous question, answer the following.

The 90% confidence interval for the average reading score of students in that Portland high school

Group of answer choices

84  ±1.645*1.6

78  ± 1.96*1.6

78  ± 1.96*8

84  ± 1.711*1.6

 

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Question 1610 pts

Perform a hypothesis test to answer the question of interest.

In the space provided show any work necessary to support how to arrived at your conclusion. In addition to your shown work, please provide the conclusion to the test. Based on the confidence interval and values in the hypotheses, what can be concluded?

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Question 172 pts

Use the following to answer the next 4 questions. A behavioral economist is interested in learning how women spend money. He randomly recruits 50 women and divides them evenly into 2 groups (25 people in each group).

Both groups receive a total of $100 dollars to spend freely in a shopping mall. Each woman in Group I receives a $100 bill, while each woman in Group II receives ten $10 bills. They can spend that $100 in whatever they want on the day of the study and whatever money they have leftover can be taken home. At the end of the day, the economist records how much money people have spent during the day; and the economist wants to know whether there is evidence that average money spent on Group I (a $100 bill) differs from group II (ten $10 bills).

 

 

Which description is a FALSE description of the data?

Group of answer choices

o Group I seems to spend more money, on average, in comparison to group II.

The interquartile ranges are appear to be similar for both groups.

o The amount of money spent on both groups are approximately symmetric.

 

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Question 182 pts

Use the information from the previous problem.

Choose the appropriate the null and alternative hypothesis:

Group of answer choices

H₀:  x ¯ g r o u p 1-  x ¯ g r o u p 2= 0

H_a:  x ¯ g r o u p 1-  x ¯ g r o u p 2 ≠ 0

 

H₀: p_group1 - p_group2  ≠ 0

H_a: p_group1 - p_group2 = 0

H_o:  μ g r o u p 1 − μ g r o u p 2 ≠ 0

H_a:  μ g r o u p 1 − μ g r o u p 2 = 0

H_o:  μ g r o u p 1 − μ g r o u p 2 = 0

H_a:  μ g r o u p 1 − μ g r o u p 2  ≠ 0

 

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Question 1910 pts

Write a conclusion based on the software output for the hypothesis test. Assume  α = 0.05.  

• (4 points) Include a statement of strength in terms of the alternative hypotheses, in the context of the problem.
• (2 points) State whether we should or should not reject the null based on the significance level. 
• (2 points) State the test statistic, df and p-value. 
• (2 points) The conclusion must be in the context of the problem. 

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Question 205 pts

Estimate the parameter of interest.

Using the R output from the previous problem, interpret the confidence interval in the context of the problem.

• (1 points) Must have context and units.
• (2 points) Must include the value of the point estimate. 
• (1 points) Correct interval values and confidence level.
• (1 points) Must illustrate which group is more (or less) than the other. 

 

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Question 213 pts

Use the following to answer the next 4 questions.

A start-up news company is looking to expand their audience and is interested in studying the how many adults regularly use social media as a source of news. According to the Pew Research Center, 62% of adults get their news from social media, but researchers want to determine of this proportion is actually greater than 62% in region they plan on advertising on.

They take a random sample of 200 adults in the region they are interested in advertising in and what they use to typically get their news. A total of 137 adults reported regularly getting their news from social media.

The point estimate for this problem is:  (report your answer to 3 decimal places)

 

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Question 222 pts

Checking Conditions: We are told that the sample was randomly selected. Are the other conditions met to perform a hypothesis test for p?

Group of answer choices

Yes, the sample size is greater than 30.

Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.

Yes, the population standard deviation is known.

No, the population mean is unknown.

 

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Question 230 pts

For the hypotheses:

 H_o: p = 0.62

H_a: p > 0.62

Calculate the test statistic.

SHOW YOUR WORK.

Use symbols like +, -, * , / and sqrt() to show your work or use the equation Canvas editor. Show your work to the best of your ability.

This question is to assess your process. In the next question, you will provide your numeric answer. Partial credit may be awarded for good supporting work even though your answer is not correct.

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Question 245 pts

Enter your numeric answer for the test statistic you calculated above.  Round your answer to 3 decimal places.

 

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Question 253 pts

Which of the following graph represents the p-value for the test? 

Group of answer choices

 

 

 

 

 

 

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Question 260 pts

Suppose a researcher is estimating the proportion of trees showing signs of disease in a local forest. They randomly sample 150 trees and find that 25 of them show signs of disease.

Calculate the 95% confidence interval for p, the proportion of all trees in the forest showing signs of disease.

SHOW YOUR WORK.

Use symbols like +, -, * , / and sqrt() to show your work or use the equation Canvas editor. Do not upload a picture of your shown work.

This question is to assess your process. In the next two questions, you will provide your answers. 

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Question 273 pts

Enter the value for your lower bound. Round to 3 decimal places. 

 

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Question 283 pts

Enter the value for your upper bound. Round to 3 decimal places. 

 

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Question 294 pts

Using the confidence you calculated for the previous problem, interpret the confidence interval in the context of the problem.

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