Final exam

Which of the following is true about sampling distributions?

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

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

26. What is the value of the test statistic?

2.03

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. What is the expected number of females who said yes?

43.87

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

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) and females 58. 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

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.

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.

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 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.

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.

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 1/3

Suppose a researcher wants to test the hypothesis that u = 25 versus the alternative that u # 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.

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?

100.4

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

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

What is a significance level?

0.01

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

23. What is the chi-square contribution for females who said yes?

1.7934

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

27. Which of the following below best describes the p-value?

@ 0.02 < p-value < 0.025.

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

Census

At the beginning of a semester, an anonymous survey was conducted en 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.

Chi square test of independence

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?

Ho: y = 3.11 HA: u > 3.11

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.

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