Stats Final Exam

Use the following information for questions 28-29: Suppose you conduct a hypothesis test to determine whether or not the average height of first-grade students is less than 46 inches. You conduct this test at the 0.05 significance level and come to the conclusion that 0.05 < p-value < 0.10. 29. What is the appropriate conclusion?

The data does not provide statistically significant evidence that the average height of first-grade students is less than 46 inches.

The lengths of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with a mean of 266 days and a standard deviation of 16 days. A study enrolls a random sample of 25 pregnant women. Assuming all appropriate conditions are met, what is the probability that the average pregnancy length of the women in the study is more than 268 days?

0.2643

Consider the following set of data: 2, 3, 4. What is the standard deviation?

1.00

Use the following information for questions 44-47: Cathy wants to see if she can predict house prices based on square footage. She decides to use simple linear regression and gets the output shown below. Assuming all conditions are met, conduct the appropriate hypothesis test at the 5% level to determine if there is a positive linear relationship between square footage and house price. 46. What is the p-value?

0.0005

Brock is interested in determining if 3 different antibiotics have different recovery times. He collected data on 6 patients taking each type of antibiotic (for a total of 18 patients) and ran the test using JMP software (partial results shown in the table below). Assuming all conditions are met, conduct the appropriate hypothesis test using a significance level of 0.01. 37. What value belongs in blank space B?

2

Use the following information for questions 37-40: Brock is interested in determining if 3 different antibiotics have different recovery times. He collected data on 6 patients taking each type of antibiotic (for a total of 18 patients) and ran the test using JMP software (partial results shown in the table below). Assuming all conditions are met, conduct the appropriate hypothesis test using a significance level of 0.01. 38. What value belongs in blank space E?

43.14

You ask a sample of 155 students, "Should clinical trials on issues such as heart attacks that affect both sexes use subjects of just one sex?" The responses are in the table below. 22. What is the expected number of females who said yes?

43.87

A researcher wants to determine if a new flu vaccine protects people from the flu better than the current vaccine. He has 100 subjects for his study. He believes that sex will affect how well the vaccine works, so within these 100 subjects, splits them up into males (48 subjects) and females (52 subjects). Within each sex, he randomly assigns half of the subjects to get the new flu vaccine and the other half to get the current flu vaccine. What type of study design is this?

Experimental Study: Block Design

We would like to test if students who are in the social sciences, natural sciences, arts & humanities, and other fields spend the same amount of time studying for this course. What type of test should we use?

F-test (ANOVA)

Use the following information for questions 28-29: Suppose you conduct a hypothesis test to determine whether or not the average height of first-grade students is less than 46 inches. You conduct this test at the 0.05 significance level and come to the conclusion that 0.05 < p-value < 0.10. 28. What is the correct decision?

Fail to Reject the Null Hypothesis.

For a table of national information regarding a specific country, it is found that the correlation with Internet use is 0.545 for​ GDP, 0.734 for​ cellular-phone use, 0.664 for​ literacy, −0.893 for​ fertility, and 0.854 for CO2 emissions. Which variable has the weakest linear association with Internet​ use?

GDP has the weakest linear association with Internet use.

Use the following information for questions 24-27: The average GPA for all college students in the United States as of 2006 was 3.11. We want to test to see if the GPA of students at Texas A&M is higher than the national average. Suppose we survey 47 randomly selected students at Texas A&M and the average GPA is 3.27, with a standard deviation of 0.54. Assuming all conditions are met, conduct a hypothesis test at the 0.01 significance level. 24. What are the hypotheses?

H0: µ = 3.11 HA: µ > 3.11

Use the following information for questions 44-47: Cathy wants to see if she can predict house prices based on square footage. She decides to use simple linear regression and gets the output shown below. Assuming all conditions are met, conduct the appropriate hypothesis test at the 5% level to determine if there is a positive linear relationship between square footage and house price. 44. What are the appropriate hypotheses?

H0: β1 = 0 HA: β1 > 0

Which of the following would be the best interpretation of 99% confidence?

If we were to take 100 samples, then approximately 99 would contain the true value of the mean and approximately 1 would not.

The average on a history exam (out of 100 points) was 85, with a standard deviation of 15. What shape would you expect the distribution of grades to take?

Left Skewed.

Heights of adult American women are normally distributed with a mean of 65 inches and a standard deviation of 3.5 inches. Taylor is a 28 year old American woman. Her doctor tells her that her height is below average but less than one standard deviation away from the mean. Which of the following could potentially be the z-score of her height?

None of the above.

Which of the statements below are true if the p-value is small? 1. The parameter value indicated by the null hypothesis is not plausible. 2. The parameter value indicated by the null hypothesis is not possible. 3. The null hypothesis should be rejected in favor of the alternative hypothesis. 4. We should fail to reject the null hypothesis.

Only 1 and 3.

Anna Grace is conducting a survey of Texas A&M students. She asks them their age, gender, current GPA, major, current number of credit hours, high school GPAs, and number of days of class they missed in the last month. What kind of variable is major?

Qualitative.

Which of the following is true about sampling distributions?

Sampling distributions get closer to normality as the sample size increases.

Sarah wants to determine the average height of all students at Wittenberg University. In which of the following scenarios would Sarah be looking at the sampling distribution?

Sarah and her 20 classmates each survey 40 students at Wittenberg University and ask them their height. Each person calculates the average of their sample and Sarah looks at all these averages.

Use the following information for questions 37-40: Brock is interested in determining if 3 different antibiotics have different recovery times. He collected data on 6 patients taking each type of antibiotic (for a total of 18 patients) and ran the test using JMP software (partial results shown in the table below). Assuming all conditions are met, conduct the appropriate hypothesis test using a significance level of 0.01. 40. What is the appropriate conclusion?

The data does not provide statistical evidence of an association between antibiotic type and recovery time.

Given the regression output below for predicting the heart weight of cats from body weight, calculate the intercept. Note that the average body weight in the sample is 2.72 kg and the average heart weight is 10.63 grams.

-0.34

Use the following information for questions 24-27: The average GPA for all college students in the United States as of 2006 was 3.11. We want to test to see if the GPA of students at Texas A&M is higher than the national average. Suppose we survey 47 randomly selected students at Texas A&M and the average GPA is 3.27, with a standard deviation of 0.54. Assuming all conditions are met, conduct a hypothesis test at the 0.01 significance level. 25. What is the significance level?

0.01.

Use the following information for questions 24-27: The average GPA for all college students in the United States as of 2006 was 3.11. We want to test to see if the GPA of students at Texas A&M is higher than the national average. Suppose we survey 47 randomly selected students at Texas A&M and the average GPA is 3.27, with a standard deviation of 0.54. Assuming all conditions are met, conduct a hypothesis test at the 0.01 significance level. 27. Which of the following below best describes the p-value?

0.02 < p-value < 0.025.

Suppose a researcher wants to test the hypothesis that µ = 25 versus the alternative that µ ≠ 25 using data from a random sample of 95 people. We calculate the standardized test statistic to be 2.087. Which of the following best describes the p-value?

0.04 < p-value < 0.05.

Use the following information for questions 44-47: Cathy wants to see if she can predict house prices based on square footage. She decides to use simple linear regression and gets the output shown below. Assuming all conditions are met, conduct the appropriate hypothesis test at the 5% level to determine if there is a positive linear relationship between square footage and house price. 45. What is the significance level?

0.05

A study of moisture and mold spores showed that in general, environments with a higher moisture content had increased number of mold spores. Moisture content explained 64% of the variation in the number of mold spores. What is the numerical value of the correlation between moisture content and mold spores?

0.80

One common disease among pediatric patients is streptococcal pharyngitis (strep throat). If a pediatric patient comes into the pediatricians feeling ill, there is a 26% chance that they have strep throat. A doctor sees 7 pediatric patients on a particular day (assume these patients are independent). Consider the random variable as a binomial random variable such that X = number of pediatric patients with strep throat. What is the chance that at least one of them has strep throat?

0.878

An index that is a standardized measure used in observing infants over time is approximately normal with a mean of 96 and a standard deviation of 10. What index score is less than 33​% of the population index scores?

100.40

The boxplot below shows the distribution of heights of 16 undergraduate statistics students. Using this boxplot, approximately how many students are 64 inches or taller?

12

Use the following information for questions 24-27: The average GPA for all college students in the United States as of 2006 was 3.11. We want to test to see if the GPA of students at Texas A&M is higher than the national average. Suppose we survey 47 randomly selected students at Texas A&M and the average GPA is 3.27, with a standard deviation of 0.54. Assuming all conditions are met, conduct a hypothesis test at the 0.01 significance level. 26. What is the value of the test statistic?

2.03.

Use the following information for questions 44-47: Cathy wants to see if she can predict house prices based on square footage. She decides to use simple linear regression and gets the output shown below. Assuming all conditions are met, conduct the appropriate hypothesis test at the 5% level to determine if there is a positive linear relationship between square footage and house price. 47. Cathy's house is 2034 square feet and costs $151,000. What is the residual for Cathy's house?

21,398.20

Use the following information for questions 37-40: Brock is interested in determining if 3 different antibiotics have different recovery times. He collected data on 6 patients taking each type of antibiotic (for a total of 18 patients) and ran the test using JMP software (partial results shown in the table below). Assuming all conditions are met, conduct the appropriate hypothesis test using a significance level of 0.01. 39. What are the appropriate hypotheses?

H0: μAntibiotic 1 = μAntibiotic 2 = μAntibiotic 3 HA: At least one mean recovery time is different.

Which of the following correctly describes the meaning of the p-value?

The p-value is the probability we would get results like our sample (or something more extreme), given the null hypothesis is true.

Taylor Swift wants to know the proportion of her fans who listened to her new single ME! within the first hour of it being released. In order to estimate this, she takes a sample of 150 of her fans and asks them if they listened to the song in this time period. Of the 150 fans, 135 of them (90%) responded that they did listen to the song during this time period. What is the parameter and what is its value?

The parameter is the proportion of all Taylor Swift fans who listened to ME! within the first hour after it was released, which is unknown.

The scatterplot below shows an outlier in the bottom left. What kind of outlier is this point?

The point is both a high leverage point and an influential point.

The scatterplot below shows the relationship between the percent of families that own their home and the percent of the population living in urban areas for each state. A residual plot is also shown. Based on the residual plot, what do you observe and what does that tell you about if a least-squares regression line is appropriate for this data?

The residuals appear to be fan shaped, indicating non-constant variance, so a least-squares regression line is not appropriate for this data.

We are testing the following hypotheses: H0: μ = 0.5 HA: μ ≠ 0.5 The sample size is 26. The test statistic is calculated as T = 2.385. What is the p-value?

between 0.02 and 0.04

A health study reported​ that, in one​ country, systolic blood pressure readings have a mean of 122 and a standard deviation of 15. A reading above 140 is considered to be high blood pressure. If the systolic blood pressure in that country has a normal​ distribution, using the z-table, what proportion of the population suffers from high blood​ pressure?

0.1151

Use the following information for questions 22-23: You ask a sample of 155 students, "Should clinical trials on issues such as heart attacks that affect both sexes use subjects of just one sex?" The responses are in the table below. 23. What is the chi-square contribution for females who said yes?

1.7934

Anna teaches a small class of 14 students. She recently gave them an exam (out of 100 points). The scores on the exam were: 0, 15, 58, 75, 78, 82, 84, 84, 89, 91, 94, 98, 100, and 100. How many of the scores are potential outliers?

2

At the beginning of a semester, an anonymous survey was conducted on students in a statistics class. Two of the questions on the survey were about gender and whether or not students have equal, more, or less energy in the afternoon compared to the morning. Below are the results. EqualLessMoreFemale183724Male91523 What test should we perform to see if gender and energy level are associated?

Chi-square test of independence.

Marco's mom has measured his height in centimeters every few months between the ages of 4.5 and 7.5. The recorded values are best estimated by the regression line with the equation ŷ = 80.46 + 6.25x. Marco's mom wants to use this equation to predict if Marco will be taller than her when he is 14 years old. Doing this prediction is an example of what?

Extrapolation

A recent study compared tooth health and periodontal damage in a group of 46 young adult males wearing a tongue piercing and a control group of 46 young adult males without a tongue piercing. One question of interest was whether individuals with tongue piercings had more enamel cracks on average. The summary statistics for the study are shown in the table below (note: not all information in the table is required to solve the problem; you must decide what pieces of information are necessary). Assuming all conditions are met, what is the 99.5% confidence interval for the difference between the number of enamel cracks in the two groups (difference = Tongue Piercing - No Tongue Piercing).

(1.1645, 4.4355)

In which of the following study designs would you generally know the value of the parameter?

Census.

One treatment for strep throat is a tonsillectomy (having the tonsils removed). A research study wanted to determine whether or not having a tonsillectomy reduced the occurrence of strep throat in pediatric patients. They recruited 40 pediatric patients who had a tonsillectomy for their study and for each patient measured both the number of occurrences of strep throat in the year prior to the tonsillectomy (untreated) and the number of occurrences of strep throat in the year following the tonsillectomy (treated). The summary statistics for the study is shown in the table below (note: not all information in the table is required to solve the problem; you must decide what pieces of information are necessary). Assuming all conditions are met, conduct the appropriate hypothesis test at the 0.01 significance level to determine if patients have less cases of strep throat after treatment [difference = untreated (before tonsillectomy) - treated (after tonsillectomy)]. 33. What is the following best describes the p-value?

p-value < 0.0005

One treatment for strep throat is a tonsillectomy (having the tonsils removed). A research study wanted to determine whether or not having a tonsillectomy reduced the occurrence of strep throat in pediatric patients. They recruited 40 pediatric patients who had a tonsillectomy for their study and for each patient measured both the number of occurrences of strep throat in the year prior to the tonsillectomy (untreated) and the number of occurrences of strep throat in the year following the tonsillectomy (treated). The summary statistics for the study is shown in the table below (note: not all information in the table is required to solve the problem; you must decide what pieces of information are necessary). Assuming all conditions are met, conduct the appropriate hypothesis test at the 0.01 significance level to determine if patients have less cases of strep throat after treatment [difference = untreated (before tonsillectomy) - treated (after tonsillectomy)]. 32. What is the value of the test statistic?

9.6838

Rock-paper-scissors is a hand game played by two or more people where players choose to sign either rock, paper, or scissors with their hands. We would like to test if players choose between these three options randomly, or if certain options are favored above others. What hypothesis test should we conduct to answer this research question?

Chi square test of goodness of fit

One treatment for strep throat is a tonsillectomy (having the tonsils removed). A research study wanted to determine whether or not having a tonsillectomy reduced the occurrence of strep throat in pediatric patients. They recruited 40 pediatric patients who had a tonsillectomy for their study and for each patient measured both the number of occurrences of strep throat in the year prior to the tonsillectomy (untreated) and the number of occurrences of strep throat in the year following the tonsillectomy (treated). The summary statistics for the study is shown in the table below (note: not all information in the table is required to solve the problem; you must decide what pieces of information are necessary). Assuming all conditions are met, conduct the appropriate hypothesis test at the 0.01 significance level to determine if patients have less cases of strep throat after treatment [difference = untreated (before tonsillectomy) - treated (after tonsillectomy)]. 31. What are the hypotheses?

H0: μd = 0 HA: μd > 0

The 99.7% confidence interval for the mean length of frog jumps is (12.64 cm, 14.44 cm). Which of the following statements is a correct interpretation of 99.7% confidence?

If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.